2024 |
| Kanovei V., Lyubetsky V., Jensen Reals by Means of Second-Order Peano Arithmetic.
Axioms, 2024, 13(2), Article no 96.
DOI: 10.3390/axioms13020096 (WoS Q2) http://iitp.ru/https://doi.org/10.3390/axioms13020096 |
| Kanovei V., Lyubetsky V., A good lightface Δ^1_n well-ordering of the reals does not imply the existence of boldface Δ^1_{n−1} well-orderings.
Annals of Pure and Applied Logic,
2024, 175, 6, pp.\ 1-38. DOI 10.1016/j.apal.2024.103426
(WoS Q2) http://iitp.ru/https://doi.org/10.1016/j.apal.2024.103426 |
| Kanovei V., Lyubetsky V., Parameterfree Comprehension does not imply full Comprehension in second order Peano arithmetic.
Studia Logica,
2024, DOI: 10.1007/s11225-024-10108-2
(WoS Q2) http://iitp.ru/https://doi.org/10.1007/s11225-024-10108-2 |
2023 |
| Lyubetsky V., Rubanov L., Tereshina M., Ivanova A., Araslanova K., Uroshlev L., Goremykina G., Yang J., Kanovei V., Zverkóv O., Shitikov A., Korotkova D., Zaraisky A., Wide-scale identification of novel/eliminated genes responsible for evolutionary transformations.
Biology Direct, 2023, Vol. 18, Art. 45.
DOI: 10.1186/s13062-023-00405-6
(WoS Q2) http://iitp.ru/https://doi.org/10.1186/s13062-023-00405-6 |
| Kanovei V., Lyubetsky V., A model in which well-orderings of the reals first appear at a given
projective level, part III, the case of second-order PA.
Mathematics,
2023, 11(15), Article no. 3294.
DOI 10.3390/math11153294
(WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/11/15/3294 |
| Kanovei V., Lyubetsky V., A model in which well-orderings of the reals first appear at a given projective level, part II.
Mathematics,
2023, 11(11), Article no. 2517. DOI: 10.3390/math11112517 .
(WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/11/11/2517 |
| Kanovei V., Lyubetsky V., On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic.
Mathematics,
2023, 11 (3), Article no. 726.
DOI: 10.3390/math11030726
(WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/11/3/726 |
| Kanovei V., Lyubetsky V., On Russell typicality in Set Theory.
Proceedings of the American Mathematical Society, 2023, 151, no 5, pp. 2201–2210.
https://doi.org/10.1090/proc/16232 (WoS Q2)
http://iitp.ru/https://www.ams.org/journals/proc/0000-000-00/S0002-9939-2023-16232-2/ |
2022 |
| Kanovei V., Lyubetsky V., On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic.
Preprints,
2022, no 2022120255.
DOI: 10.20944/preprints202212.0255.v2 http://iitp.ru/https://www.preprints.org/manuscript/202212.0255/v2 |
| Kanovei V., On sets that hereditarily belong to countable OD sets.
European Set Theory Conference 2022. Department of Mathematics of the University of Turin and the European Set Theory Society, August 29 - September 2, 2022, Turin, Italy. http://logicgroup.altervista.org/torino/ESTC2022/site/abstracts/ |
| Kanovei V., Lyubetsky V., The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic. arXiv: 2209.07599 [math.LO], September 2022. http://iitp.ru/https://arxiv.org/pdf/2209.07599.pdf |
| Kanovei V., Lyubetsky V., A model in which wellorderings of the reals appear at a given projective level.
Axioms, 2022, 11(8), Article no 354.
DOI: 10.3390/axioms11080354
(WoS Q2) http://iitp.ru/https://doi.org/10.3390/axioms11080354 |
| Kanovei V., Lyubetsky V., A model in which the Separation principle holds for a given effective projective Sigma-class.
arXiv: 2204.03915 [math.LO], April 2022. http://iitp.ru/https://arxiv.org/abs/2204.03915 |
| Kanovei V., Lyubetsky V., On the ‘definability of definable’ problem of Alfred Tarski, Part II.
Transactions of the American Mathematical Society,
2022, Vol. 375, No. 12, P. 8651–8686.
DOI: 10.1090/tran/8710
(WoS Q2) http://iitp.ru/https://doi.org/10.1090/tran/8710 |
| Kanovei V., Lyubetsky V., A model in which the separation principle holds for a given effective projective Sigma-class.
Axioms, 2022, 11, Issue 3, Paper no. 122.
DOI 10.3390/axioms11030122
(WoS Q2) http://iitp.ru/https://www.mdpi.com/2075-1680/11/3/122 |
| Kanovei V., Lyubetsky V., A generic model in which the Russell-nontypical sets satisfy ZFC strictly between HOD and the universe.
Mathematics, 2022, 10, Issue 3, Paper no. 491, DOI 10.3390/math10030491
(WoS Q1) http://iitp.ru/https://doi.org/10.3390/math10030491 |
2021 |
| Kanovei V., On the ‘Definability of definable’ problem of Alfred Tarski.
Logic Colloquium 2021. European Summer Meeting of the Association for Symbolic Logic. Book of abstracts. S.Chlebowski, D.Ratajczyk, P.Lupkowski (eds.) Adam Mickiewicz University, Poznan, Poland, 19-24 July 2021. Page 195. |
| Kanovei V., Lyubetsky V., On Russell typicality in Set Theory. arXiv: 2111.07654 [math.LO], November 2021. http://iitp.ru/https://arxiv.org/abs/2111.07654 |
| Kanovei V., Lyubetsky V., A product forcing model in which the Russell-nontypical sets satisfy ZFC strictly between HOD and the universe. arXiv: 2111.13491 [math.LO], November 2021. http://iitp.ru/https://arxiv.org/abs/2111.13491 |
| Kanovei V., Paradoxical partitions of the reals by Robert Solovay.
International Conference "Adian 90: Conference on Mathematical Logic, Algebra and Computation" 7 July 2021, 12:45–13:30, Steklov Math. Inst. (Moscow). http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=31068 |
| Enayat A., Kanovei V., Lyubetsky V., On effectively indiscernible projective sets and the Leibniz-Mycielski axiom.
Mathematics, 2021, Vol. 9, No. 14, Art. 1670.
DOI: 10.3390/math9141670
(WoS Q1) http://iitp.ru/https://doi.org/10.3390/math9141670 |
| Enayat A., Kanovei V., An unpublished theorem of Solovay, on OD partitions of reals into two non-OD parts, revisited.
Journal of Mathematical Logic, 2021, vol. 21, Issue 03, Article No. 2150014 DOI: 10.1142/S0219061321500148 WoS Q1. http://iitp.ru/https://www.worldscientific.com/doi/10.1142/S0219061321500148 |
| Kanovei V., Lyubetsky V., Models of set theory in which separation theorem fails.
Izvestiya: Mathematics, 2021, Vol. 85, No 6,1181-1219.
DOI: https://doi.org/10.1070/IM8937
(WoS Q2) http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=8937&option_lang=rus |
| Kanovei V., Schindler R., Definable Hamel bases and ACω(R).
Fundamenta Mathematicae, 2021, 253, 3, p. 239-256. DOI 10.4064/fm909-6-2020 WoS Q3 http://iitp.ru/https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/online/113667/d |
| Kanovei V., Lyubetsky V., Factoring Solovay-random extensions, with application to the Reduction property.
Monatshefte fur Mathematik, 2021, 194, 1, pp. 105–117.
DOI: 10.1007/s00605-020-01482-9
(WoS Q2) http://iitp.ru/https://doi.org/10.1007/s00605-020-01482-9 |
| Kanovei V., Lyubetsky V., The full basis theorem does not imply analytic wellordering,
Annals of pure and applied logic, 2021, volume 172, issue 4, paper no 102929.
DOI: 10.1016/j.apal.2020.102929
(WoS Q1) http://iitp.ru/https://www.sciencedirect.com/science/article/pii/S0168007220301536?via%3Dihub |
2020 |
| Enayat A., Kanovei V., An unpublished theorem of Solovay, revisited. arXiv:2001.11058 [math.LO], January 2020. http://iitp.ru/https://arxiv.org/abs/2001.11058 |
| Kanovei V., Lyubetsky V., On the "definability of definable" problem of Alfred Tarski.
Mathematics, 2020, Vol. 8, No. 12, Art. 2214.
DOI: 10.3390/math8122214
(WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/8/12/2214 |
| Kanovei V., Lyubetsky V., On the Δ1n Problem of Harvey Friedman.
Mathematics,
2020, Vol. 8, No. 9, Art. 1477.
DOI: 10.3390/math8091477
(WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/8/9/1477 |
| Kanovei V., Lyubetsky V., On the equality modulo a countable set.
Mathematical notes,
2020, Vol. 108, Iss. 4, P. 615–616.
DOI: 10.1134/S0001434620090357 http://mi.mathnet.ru/mz12753 |
| Kanovei V., Lyubetsky V., Models of set theory in which nonconstructible reals first appear at a given projective level .
Mathematics, 2020, Vol. 8, No. 6, Art. 910. DOI: 10.3390/math8060910 (WoS Q1) http://iitp.ru/https://www.mdpi.com/2227-7390/8/6/910 |
| Kanovei V., Katz M., Nowik T., Metric completions, Heine-Borel, and approachability.
Open Mathematics, 2020, Volume 18, Issue 1, 162-166. DOI: 10.1515/math-2020-0017 WoS Q3 http://iitp.ru/https://www.degruyter.com/view/journals/math/18/1/article-p162.xml?tab_body=abstract |
| Bair J., Blaszczyk P., Heinig P., Kanovei V., Katz M., McGaffey T., Cauchy"s work on integral geometry, centers of curvature, and other applications of infinitesimals.
Real Analysis Exchange, 2020, Vol. 45, No. 1, pp. 127-150 . DOI: 10.14321/realanalexch.45.1.0127 http://iitp.ru/https://www.jstor.org/stable/10.14321/realanalexch.45.1.0127?seq=1 |
| Kanovei V., Lyubetsky V., Canonization of smooth equivalence relations on infinite-dimensional E0-large products.
Notre Dame Journal of Formal Logic,
2020, Vol. 61, No. 1, P. 117–128.
DOI: 10.1215/00294527-2019-0034
(WoS Q1) http://iitp.ru/https://projecteuclid.org/euclid.ndjfl/1576120172 |
2019 |
| Lyubetsky V., Kanovei V., Set theory: absolute undecidability of classical problems.
Textbook for universities, 2nd ed., Moscow, Urait, 2019, 348 p. (in Russian).
ISBN: 978-5-534-10390-8 |
| Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., Kutateladze S., Nowik T., Schaps D., Sherry D., Gregory’s Sixth Operation.
Mircea Pitici (Editor), The Best Writing on Mathematics 2019 Princeton University Press, 2019, pp. 195–207. DOI: 10.1515/9780691197944-015 Book DOI: 10.1515/9780691197944 Online ISBN: 9780691197944 http://iitp.ru/https://doi.org/10.1515/9780691197944-015 |
| Bair J., Blaszczyk P., Kanovei V., Katz M., Heinig P., 19th-century real analysis, forward and backward.
Antiquitates Mathematicae, 2019, 13, 1, pp. 19-49. DOI:10.14708/am.v13i1.6440 http://iitp.ru/https://wydawnictwa.ptm.org.pl/index.php/antiquitates-mathematicae/article/view/6440 |
| Kanovei V., Lyubetsky V., Indiscernible pairs of countable sets of reals at a given projective level.
arXiv: 1912.12962 [math.LO], December 2019. http://iitp.ru/https://arxiv.org/abs/1912.12962 |
| Kanovei V., Definable selector for Δ02 sets modulo countable.
arXiv: 1910.00926 [math.LO], October 2019 http://iitp.ru/https://arxiv.org/abs/1910.00926 |
| Bottazzi E., Kanovei V., Katz M., Mormann T., Sherry D., On mathematical realism and applicability of hyperreals.
Matematychni Studii, 2019, 51, 2, pp. 200-224. DOI:10.15330/ms.51.2.200-224 SCIMAGO, Q3 http://iitp.ru/https://doi.org/10.15330/ms.51.2.200-224 |
| Kanovei V., Lyubetsky V., Models of set theory in which separation theorem fails.
arXiv:1905.11241 [math.LO], May 2019. http://iitp.ru/https://arxiv.org/abs/1905.11241 |
| Kanovei V., Lyubetsky V., Absoluteness of the Solovay set Σ.
Siberian Mathematical Journal,
2019, 60, no 6, pp. 1003-1006.
DOI: 10.1134/S0037446619060089
(WoS Q3) http://mi.mathnet.ru/rus/smj/v60/i6/p1286 |
| Gitman V., Friedman S.D., Kanovei V., A model of second-order arithmetic satisfying AC but not DC.
Journal of Mathematical Logic, 2019, 19, no 1, article ID 1850013, pp. 1--39. DOI 10.1142/S0219061318500137 WoS Q1 (Ranked 1st overall in the category of Logic) http://iitp.ru/https://www.worldscientific.com/doi/pdf/10.1142/S0219061318500137 |
| Kanovei V., Lyubetsky V., Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
Fundamenta mathematicae,
2019, 245, 2, pp. 175--216.
DOI: 10.4064/fm517-7-2018
(WoS Q3) http://iitp.ru/https://www.doi.org/10.4064/fm517-7-2018 |
| Kanovei V., Lyubetsky V., Definable elements of definable Borel sets.
Mathematical Notes,
2019, 105, no 5, pp. 684-693.
DOI: 10.1134/S0001434619050055
(WoS Q3) http://mi.mathnet.ru/mz12001 |
| Kanovei V., Lyubetsky V., Borel OD sets of reals are OD-Borel in some simple models.
Proceedings of the American mathematical society,
2019, 147, no 3, pp. 1277–1282.
DOI 10.1090/proc/14286
(WoS Q2) http://iitp.ru/https://doi.org/10.1090/proc/14286 |
| Kanovei V., Lyubetsky V., Definable minimal collapse functions at arbitrary projective levels.
Journal of Symbolic Logic,
2019, vol. 84, no 1, pp. 266-289.
DOI:10.1017/jsl.2018.77
(WoS Q2) http://iitp.ru/https://doi.org/10.1017/jsl.2018.77 |
2018 |
| Kanovei V., Lyubetsky V., Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v3 [math.LO], January 2018. http://iitp.ru/https://arxiv.org/abs/1712.00769v3 |
| Kanovei V., Lyubetsky V., On intermediate extensions of generic extensions by a random real.
arXiv:1811.10568 [math.LO], December 2018. http://iitp.ru/https://arxiv.org/abs/1811.10568 |
| Kanovei V., Lyubetsky V., On Harrington"s model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami.
arXiv:1810.12542v2 [math.LO], November 2018. http://iitp.ru/https://arxiv.org/abs/1810.12542 |
| Kanovei V., Lyubetsky V., A countable definable set of reals containing no definable elements,
arXiv:1408.3901v2 [math.LO], Sept. 2018, 11 p.
http://iitp.ru/https://arxiv.org/abs/1408.3901 |
| Gitman V., Friedman S.D., Kanovei V., A model of second-order arithmetic satisfying AC but not DC.
arXiv:1808.04732 [math.LO], August 2018. http://iitp.ru/https://arxiv.org/abs/1808.04732 |
| Kanovei V., Lyubetsky V., Definable E0 classes at arbitrary projective levels.
Annals of Pure and Applied Logic,
2018, Vol. 169, Iss. 9, P. 851–871.
DOI: 10.1016/j.apal.2018.04.006
(WoS Q1) http://iitp.ru/https://doi.org/10.1016/j.apal.2018.04.006 |
| Kanovei V., Lyubetsky V., Canonization of smooth equivalence relations on infinite-dimensional perfect cubes.
arXiv:1804.05174 [math.LO], April 2018. http://arxiv.org/abs/1804.05174 |
| Kanovei V., Katz M., Blaszczyk P., Nowik T., Monotone subsequence via ultrapower.
Open Mathematics, 2018, 16, 1, c. 149-153 DOI: 10.1515/math-2018-0015 WoS Q2 http://iitp.ru/https://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0015/math-2018-0015.xml |
| Kanovei V., Katz K., Katz M., Mormann T., What makes a theory of infinitesimals useful? A view by Klein and Fraenkel.
Journal of Humanistic Mathematics, 2018, 8, 1, pp. 108-119. DOI: 10.5642/jhummath.201801.07 http://scholarship.claremont.edu/jhm/vol8/iss1/7 |
| Bascelli T., Blazczyk P., Borovik A., Kanovei V., Katz K., Katz M., Kutateladze S., McCaffery T., Schaps D., Sherry D., Cauchy"s infinitesimals, his sum theorem, and foundational paradigms.
Foundations of Science, 2018, 23, 2, pp 267–296. DOI: 10.1007/s10699-017-9534-y WoS Q2 http://link.springer.com/article/10.1007/s10699-017-9534-y |
| Kanovei V., Lyubetsky V., Countable OD sets of reals belong to the ground model.
Archive for Mathematical Logic,
2018, Vol. 57, Iss. 3–4, P. 285–298.
DOI: 10.1007/s00153-017-0569-0 http://link.springer.com/article/10.1007/s00153-017-0569-0 |
| Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., et al., Gregory"s sixth operation,
Foundations of Science, 2018, 23, 1, pp. 133--144. DOI: 10.1007/s10699-016-9512-9 WoS Q2 http://link.springer.com/article/10.1007/s10699-016-9512-9 |
| Herzberg F., Kanovei V., Katz M., Lyubetsky V., Minimal axiomatic frameworks for definable hyperreals with transfer.
Journal of Symbolic Logic,
2018, 83, 1, pp. 385-391.
DOI: 10.1017/jsl.2017.48
(WoS Q1)
http://iitp.ru/https://doi.org/10.1017/jsl.2017.48 |
| Kanovei V., Lyubetsky V., Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes.
Izvestiya: Mathematics,
2018, Vol. 82, No. 1, P. 61–90.
DOI: 10.1070/IM8521
(WoS Q2) http://mi.mathnet.ru/izv8521 |
2017 |
| Herzberg F., Kanovei V., Katz M., Lyubetsky V., Minimal axiomatic frameworks for definable hyperreals with transfer.
arXiv:1707.00202 [math.LO], July 2017. http://iitp.ru/https://arxiv.org/abs/1707.00202 |
| Bair J., Blaszczyk P., Ely R., Henry V., Kanovei V., Katz K., Katz M., Kudryk T., Kutateladze S., McGaffey T., Mormann T., Schaps D., Sherry D., Cauchy, infinitesimals and ghosts of departed quantifiers,
Mat. Stud. 2017, 47, 2, 115--144 doi:10.15330/ms.47.2.115-144 http://matstud.org.ua/texts/2017/47_2/115-144.pdf |
| Kanovei V., Lyubetsky V., Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v1 [math.LO], December 2017. http://iitp.ru/https://arxiv.org/abs/1712.00769v1 |
| Kanovei V., Lyubetsky V., Definable minimal collapse functions at arbitrary projective levels.
arXiv:1707.07320 [math.LO], July 2017. http://iitp.ru/https://arxiv.org/abs/1707.07320 |
| Kanovei V., Lyubetsky V., Definable E0 classes at arbitrary projective levels.
arXiv:1705.02975 [math.LO], May 2017. http://iitp.ru/https://arxiv.org/abs/1705.02975 |
| Kanovei V., Lyubetsky V., The full basis theorem does not imply analytic wellordering.
arXiv:1702.03566v2 [math.LO], February 2017. http://iitp.ru/https://arxiv.org/abs/1702.03566 |
| Kanovei V., Lyubetsky V., A generic property of the Solovay set Σ.
Siberian Mathematical Journal,
2017, Vol. 58, Iss. 6, P. 1012–1014.
doi:10.1134/S0037446617060106 http://iitp.ru/https://link.springer.com/article/10.1134%2FS0037446617060106 |
| Fletcher P., Hrbacek K., Kanovei V., Katz M., Lobry C., Sanders S., Approaches to analysis with infinitesimals following Robinson, Nelson, and others.
Real Analysis Exchange, 2017, 42, 2, pp. 193-252. DOI: 10.14321/realanalexch.41.1.0193 SCIMAGO, Q3 http://iitp.ru/https://www.jstor.org/stable/10.14321/realanalexch.42.2.0193?refreqid=excelsior%3Ab03b59e276fdb542e9 |
| Kanovei V., Katz M., A positive function with vanishing Lebesgue integral in Zermelo -- Fraenkel set theory.
Real Analysis Exchange, 2017, 42, no. 2, 385-390. DOI: 10.14321/realanalexch.42.2.0385 SCIMAGO, Q3 http://msupress.org/journals/issue/?id=50-21D-61F |
| Blaszczyk P., Kanovei V., Katz M., et al., Toward a history of mathematics focused on procedures,
Foundations Of Science, 2017, 22, Issue 4, pp 763–783, DOI: 10.1007/s10699-016-9498-3 . WoS Q2 http://link.springer.com/article/10.1007/s10699-016-9498-3 |
| Blaszczyk Piotr, Kanovei V., U. Katz Karin, G. Katz Mikhail, et al., Is Leibnizian calculus embeddable in first order logic?
Foundations of Science, 2017, 22, Issue 4, pp 717–731. DOI: 10.1007/s10699-016-9495-6 . WoS Q2 http://iitp.ru/https://link.springer.com/article/10.1007/s10699-016-9495-6 |
| Bair J., Blaszczyk P., Ely R., Henry V., Kanovei V., Katz K., Katz M., et al., Interpreting the infinitesimal mathematics of Leibniz and Euler,
Journal for General Philosophy of Science, 2017, 48, issue 2, pp, 195--238. DOI: 10.1007/s10838-016-9334-z . SCOPUS Q2 http://link.springer.com/article/10.1007/s10838-016-9334-z |
| Kanovei V., Lyubetsky V., A countable definable set containing no definable elements.
Mathematical Notes,
2017, Vol. 102, Iss. 3–4, P. 338–349.
doi:10.1134/S0001434617090048 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=10842&option_lang=rus |
| Blazczyk P., Kanovei V., Katz M., Sherry D., Controversies on foundations of analysis: comments on Schubring’s conflicts.
Foundations of Science, 2017, 22, 1, pp. 125--140. DOI: 10.1007/s10699-015-9473-4 . WoS Q2 http://link.springer.com/article/10.1007/s10699-015-9473-4?no-access=true |
| Golshani M., Kanovei V., Lyubetsky V., A Groszek-Laver pair of undistinguishable E0-classes.
Mathematical Logic Quarterly,
2017, Vol. 63, No. 1–2, P. 19–31.
doi:10.1002/malq.201500020 http://onlinelibrary.wiley.com/wol1/doi/10.1002/malq.201500020/abstract |
2016 |
| Golshani M., Kanovei V., Lyubetsky V., A Groszek-Laver pair of undistinguishable E0 classes.
arXiv:1601.03477 [math.LO], Jan 14 2016, 18 pp. http://iitp.ru/https://arxiv.org/abs/1601.03477 |
| Kanovei V., Lyubetsky V., A generic property of Solovay"s set Σ.
arXiv:1611.00176 [math.LO], November 2016, 4 pp. http://iitp.ru/https://arxiv.org/abs/1611.00176 |
| Kanovei V., Lyubetsky V., In Cohen generic extension, every countable OD set of reals belongs to the ground model.
July 2016, arXiv:1607.02880 [math.LO] pp. 1-3. http://iitp.ru/https://arxiv.org/abs/1607.02880 |
| Kanovei V., Lyubetsky V., Countable OD sets of reals belong to the ground model.
arXiv:1609.01032 [math.LO], September 2016, 12 pp. http://arxiv.org/abs/1609.01032 |
| Błaszczyk P., Borovik A., Kanovei V., Katz M., et al., A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos.
Logica Universalis, 2016, 10, pp. 393-405. DOI 10.1007/s11787-016-0153-0 SCOPUS Q3 http://link.springer.com/article/10.1007/s11787-016-0153-0?wt_mc=Internal.Event.1.SEM.ArticleAuthorO |
| Kanovei V., Katz K., Katz M., Nowik T., Small oscillations of the pendulum, Euler’s method, and adequality,
Quantum Studies: Mathematics and Foundations, 2016, 3, no 3, pp 231–236. DOI: 10.1007/s40509-016-0074-x http://link.springer.com/article/10.1007%2Fs40509-016-0074-x |
| Kanovei V., OD elements of countable OD sets in the Solovay model.
March 2016, arXiv:1603.04237 [math.LO], pp. 1-20. http://arxiv.org/abs/1603.04237 |
| Kanovei V., Some applications of finite-support products of Jensen"s minimal forcing.
Winter School in Abstract Analysis 2016, Hejnice, Czech Republic, Jan 30—Feb 6, 2016, Abstracts and slides. http://www.winterschool.eu/files/885-Some_applications_of_finite-support_products_of_Jensens_minimal_Delta_31_forcing.pdf http://www.winterschool.eu/2016/abstracts |
| Kanovei V., Lyubetsky V., Counterexamples to countable-section
Π12 uniformization and Π13 separation.
Annals of Pure and Applied Logic, 2016, 167, 3, pp. 262–283. DOI: 10.1016/j.apal.2015.12.002 (WoS Q1) http://www.sciencedirect.com/science/article/pii/S0168007215001268 |
| Kanovei V., Lyubetsky V., On countable cofinality and decomposition of definable thin orderings.
Fundamenta mathematicae, 2016, 235, no 1, pp. 13-36.
DOI: 10.4064/fm977-10-2015 http://iitp.ru/https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/online/91557/on |
| Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., et al., Leibniz vs Ishiguro: closing a quarter-century of syncategoremania.
The Journal of the International Society for the History of Philosophy of Science,
2016, 6, no 1, pp. 117 -- 147.
DOI: 10.1086/685645 http://www.journals.uchicago.edu/doi/10.1086/685645 |
2015 |
| Kanovei V., Some applications of finite-support products of Jensen’s minimal forcing.
Book of abstracts, Logic Colloquium 2015, Annual European Summer Meeting of the Association for Symbolic Logic,
University of Helsinki, 3–8 August 2015, pp. 670-671. http://www.helsinki.fi/lc2015/materials/CLMPS_LC_book of abstracts 29.7.2015.pdf |
| Kanovei V., Lyubetsky V., Grossone approach to Hutton and Euler transforms.
Applied Mathematics and Computation,
2015, 255, pp. 36–43.
DOI: 10.1016/j.amc.2014.06.037
(WoS Q1) http://dx.doi.org/10.1016/j.amc.2014.06.037 |
| Kanovei V., Katz K., Katz M., Sherry D., Euler"s lute and Edward"s oud.
Mathematical Intelligencer, 2015, 37, 4, pp. 48--51.
DOI: 10.1007/s00283-015-9565-6 SCIMAGO, Q2 http://dx.doi.org/10.1007/s00283-015-9565-6 |
| Kanovei V., Lyubetsky V., A definable E0 class containing no definable elements.
Archive for Mathematical Logic,
2015, 54, 5, pp. 711–723.
DOI: 10.1007/s00153-015-0436-9 http://link.springer.com/article/10.1007/s00153-015-0436-9 |
| Kanovei V., Lyubetsky V., Generalization of one construction by Solovay.
Siberian Mathematical Journal,
2015, 56, no. 6, pp. 1072–1079.
DOI: 10.1134/S0037446615060117 http://iitp.ru/https://link.springer.com/article/10.1134/S0037446615060117 |
| Kanovei V., Katz Ê., Katz M., Schaps D., Proofs and retributions,
Foundations of Science, 2015, 20, 1, pp 1-25.
DOI: 10.1007/s10699-013-9340-0 SCIMAGO, Q2 http://link.springer.com/article/10.1007%2Fs10699-013-9340-0 |
| Kanovei V., Lyubetsky V., On effective σ-boundedness and σ-compactness in Solovay"s model,
Mathematical notes,
2015, 98, 1-2, pp. 273--282.
DOI: 10.1134/S0001434615070299 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=10415&option_lang=rus |
2014 |
| Kanovei V., Lyubetsky V., On countable cofinality and decomposition of definable thin orderings, arXiv:1412.0195 [math.LO], Dec. 2014, 21 p.
http://arxiv.org/abs/1412.0195 |
| Kanovei V., Lyubetsky V., Counterexamples to countable-section Π12 uniformization and Π13 separation, arXiv:1410.2537 [math.LO], Oct. 2014, 18 p. http://arxiv.org/abs/1410.2537 |
| Kanovei V., Lyubetsky V., A definable $E_0$-class containing no definable elements, arXiv:1408.6642 [math.LO], Aug 2014, 12 p. http://arxiv.org/abs/1408.6642 |
| Kanovei V., Lyubetsky V., A countable definable set of reals containing no definable elements,
arXiv:1408.3901 [math.LO], Aug. 2014, 11 p. http://arxiv.org/abs/1408.3901 |
| Kanovei V., Lyubetsky V., Linearization of partial quasi-orderings in the Solovay model revisited, arXiv:1408.1202 [math.LO], Aug. 2014, 13 p. http://arxiv.org/abs/1408.1202 |
| Kanovei V., Bounding and decomposing thin analytic partial orderings, arXiv:1407.0929v2 [math.LO], Jul 2014, 12 p. http://arxiv.org/abs/1407.0929 |
| Kanovei V., A generalization of Solovay"s Sigma-construction. arXiv:1402.0961 [math.LO]. 5 Feb 2014, 6 p. http://arxiv.org/abs/1402.0961 |
| Kanovei V., On the automorphisms behind the Gitik -- Koepke model. In:
Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch.
College publications, London, 2014, SeriesTributes, Vol. 23, pp. 229--253
http://iitp.ru/https://zbmath.org/?q=an%3A1358.03074 |
| Bascelli T., Kanovei V., Katz K., Katz M., et al., Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow.
Notices of the AMS, 2014, 61, 8, pp. 848--864.
DOI: 10.1090/noti1149 SCIMAGO, Q3 http://www.ams.org/notices/201408/rnoti-p848.pdf |
2013 |
| Kanovei V., On countable cofinality of definable chains in Borel partial orders.
arXiv:1312.2064 [math.LO].
Sat, 7 Dec 2013 http://arxiv.org/abs/1312.2064 |
| Kanovei V., Surreal numbers from the point of view of nonstandard analysis,
Sy David Friedman"s 60th-Birthday Conference, Vienna, Austria, July 2013. http://www.logic.univie.ac.at/2013/SDF60/Abstracts.html#Kanovei |
| Felgner U., Kanovei V., Koepke P., Purkert W., editors ., Felix Hausdorff.
Gesammelte Werke, Band IA: Allgemeine Mengenlehre.
Berlin: Springer, 2013, xxvi+538 pp., Monograph
ISBN: 978-3-642-25598-4. http://www.springer.com/mathematics/history+of+mathematics/book/978-3-642-25598-4 |
| Bair J., Blazczyk P., Ely R., Henry V., Kanovei V., et al., Is mathematical history written by the victors?
Notices of the AMS, 2013, 60, no 7, pp. 886-904.
DOI: 10.1090/noti1026 SCIMAGO, Q3 http://www.ams.org/notices/201307/rnoti-p886.pdf |
| Kanovei V., Sabok M., Zapletal J., Canonical Ramsey Theory on Polish Spaces.
Cambridge University Press, Cambridge, UK, 2013, viii+269 pp.,
Monograph ISBN 978-1-107-02685-8 http://www.cambridge.org/9781107026858 |
| Kanovei V., Lyubetsky V., Contemporary Set Theory: absolutely undecidable classical problems. (Russian.) Monograph, published by Independent Moscow university, 2013, 384 pages. http://biblio.mccme.ru/node/2878 |
| Kanovei V., Kommentar zu [H 1936b], Summen von $aleph_1$ Mengen.
In: Felix Hausdorff,
Gesammelte Werke. Band Ia: Allgemeine Mengenlehre,
Berlin: Springer, 2013, pp. 364-366.
http://www.amazon.ca/Felix-Hausdorff-Gesammelte-Allgemeine-Mengenlehre/dp/toc/3642255981 |
| Kanovei V., Kommentar zu [H 1909a], Die Graduierung nach dem Endverlauf.
In: Felix Hausdorff,
Gesammelte Werke. Band Ia: Allgemeine Mengenlehre,
Berlin: Springer, 2013, pp. 336-346.
http://www.amazon.ca/Felix-Hausdorff-Gesammelte-Allgemeine-Mengenlehre/dp/toc/3642255981 |
| Kanovei V., Gaps in partially ordered sets and related problems,
In: Felix Hausdorff,
Gesammelte Werke. Band Ia: Allgemeine Mengenlehre,
Berlin: Springer, 2013,
pp. 367-405. http://www.amazon.ca/Felix-Hausdorff-Gesammelte-Allgemeine-Mengenlehre/dp/toc/3642255981 |
| Kanovei V., Lyubetsky V., On effective $sigma$-boundedness and $sigma$-compactness,
Mathematical Logic Quarterly,
2013, 59, no 3,
pp. 147-166.
doi: 10.1002/malq.201200001 http://onlinelibrary.wiley.com/doi/10.1002/malq.201200001/full |
| Kanovei V., Katz M., Mormann T., Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics,
Foundations of Science, 2013, 18, 2, pp. 259-296.
DOI 10.1007/s10699-012-9316-5 http://dx.doi.org/10.1007/s10699-012-9316-5 |
2012 |
| Kanovei V., Lyubetsky V., “Effective Compactness and Sigma-Compactness”
Mathematical notes,
2012, Vol. 91, Iss. 6, P. 789–799. http://mi.mathnet.ru/rus/mz/v91/i6/p840 |
| Kanovei V., Lyubetsky V., An infinity which depends on the axiom of choice,
Applied Mathematics and Computation,
Vol. 218, Iss. 16, April 15 2012, P. 8196–8202,
http://dx.doi.org/10.1016/j.amc.2011.05.003 |
2011 |
| Kanovei V., On effective compactness and sigma-compactness.
arXiv:1103.1060 [math.LO].
Sat, 5 Mar 2011 http://arxiv.org/abs/1103.1060 |
| Kanovei V., On effective sigma-boundedness and sigma-compactness.
arXiv:1110.0919 [math.LO].
Wed, 5 Oct 2011. http://arxiv.org/abs/1110.0919 |
| Kanovei V., Lyubetsky V.A., An infinity which needs the axiom of choice,
Logic Colloquium 2011, Barcelona, 2011,
Contributed Talks. http://www.logic2011.org/Dades/TimetableContributedTalks.pdf |
| Kanovei V., On e ffective compactness and sigma-compactness,
Third European Set Theory
Conference, 3 - 8 July 2011, ICMS, Edinburgh, UK.
http://www.esf.org/serving-science/conferences/details/2011/confdetail368/368-final-programme.html |
| Kanovei V., Lyubetsky V., “An effective minimal encoding of uncountable sets”
Siberian mathematical journal,
2011, Vol. 52, No. 5, pp. 854–863. http://www.springerlink.com/content/hgwv8882kl061v70/ |
| Kanovei V., Lyubetsky V., On the infinitary pantachie of Du Bois Reymond,
Proceedings of the International Mathematical Conference “50 Years Of IITP”,
Moscow, Russia, July 25–29, 2011, 7 pages. http://iitp.ru/upload/content/839/Kanovei.pdf |
2010 |
| Kanovei V., Linear ROD subsets of Borel partial orders are countably cofinal in Solovay"s model.
arXiv:1005.5534 [math.LO].
Sun, 30 May 2010. http://arxiv.org/abs/1005.5534 |
| Kanovei V., On automorphisms behind the Gitik -- Koepke model for violation of the Singular Cardinals Hypothesis w/o large cardinals.
arXiv:1008.3471 [math.LO].
Fri, 20 Aug 2010. http://arxiv.org/abs/1008.3471 |
| Kanovei V., A weak dichotomy below E_1 * E_3,
Topology and its applications, 2010, 157, 8, pp. 1465-–1478
doi:10.1016/j.topol.2009.03.052.
http://iitp.ru/ http://dx.doi.org/10.1016/j.topol.2009.03.052 |
| Bagaria J., Kanovei V., On coding uncountable sets by reals,
Mathematical Logic Quarterly, 2010, 56, No. 4, pp. 409--424.
http://onlinelibrary.wiley.com/doi/10.1002/malq.200910056/abstract |
| Kanovei V., Lyubetsky V., Julius Koenig sets as higher infinity,
Infinite and Infinitesimal in Mathematics and Natural Sciences. International Workshop, 17-21 May 2010, Book of Abstracts, p. 27, University of Calabria, Italy, 2010. http://www.theinfinitycomputer.com/Infinity2010/Abstracts_Infinity2010.pdf |
| Kanovei V., Lyubetsky V., Contemporary Set Theory: Borel and projective sets. (Russian.)
Monograph, published by Independent Moscow university, 2010, 320 pages. http://www.mccme.ru/free-books/#kanovej |
2009 |
| Kanovei V., Lyubetsky V., Borel reducibility as an additive property of domains,
Journal of Mathematical Sciences,
2009, Vol. 158, No. 5, P. 708–712. http://www.springerlink.com/content/t61n117p753548n1/ |
| Kanovei V., On Hausdorff"s ordered structures.
Izvestiya: Mathematics, 2009, 73, 5, pp. 939--958. http://mi.mathnet.ru/rus/izv/v73/i5/p83 |
| Kanovei V., On definability of some counterexamples in descriptive set theory,
ESI Workshop on Large Cardinals and descriptive Set Theory,
Vienna, June 14--27, 2009,
Vienna, Erwin Schroedinger Institute,
2009, p. 20. http://www.logic.univie.ac.at/2009/esi/booklet.pdf |
| Kanovei V., Lyubetsky V., Reeken M., Nonstandard class and superset theories,
Logic and Mathematics, The University of York, 3-7 August, 2009.
Department of Mathematics, University of York, 2009, p. 21. http://maths.york.ac.uk/www/sites/default/files/kanovei-slides.pdf |
| Kanovei V., Lyubetsky V., Reasonable non-Radon-Nikodym ideals,
Topology and its Applications,
2009, 156, 5, pp. 911–914. http://iitp.ru/ http://dx.doi.org/10.1016/j.topol.2008.11.008 |
2008 |
| Kanovei V., Lyubetsky V., Reasonable non--Radon--Nikodym ideals.
arXiv:0806.4760 [math.LO].
Sun, 29 Jun 2008 http://arxiv.org/abs/0806.4760 |
| Felgner U., Herrlich H., Husek M., Kanovei V., et al., editors ., Felix Hausdorff.
Gesammelte Werke, Band III: Mengenlehre,
Deskriptive Mengenlehre und Topologie.
Berlin: Springer, 2008, xxii+1005 pp.,
Monograph
ISBN: 978-3-540-76806-7. http://iitp.ru/https://www.springer.com/de/book/9783540768067 |
| Herrlich H., Husek M., Kanovei V., et al., Anmerkungen der Herausgeber,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 352-398.
|
| Kanovei V., Hausdorff und Lusin,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 25-30.
|
| Kanovei V., Koepke P., Commentary to [H 1916],
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 439-442.
|
| Kanovei V., Koepke P., Commentary to [H 1933a],
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 478.
|
| Kanovei V., Koepke P., Commentary to [H 1933b],
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 482.
|
| Kanovei V., Koepke P., Commentary to [H 1935c],
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 528.
|
| Kanovei V., Koepke P., ds-Operationen, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 583-587.
|
| Kanovei V., Koepke P., Mengensysteme, Borelmengen, Trennbarkeit, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 617-625.
|
| Kanovei V., Koepke P., Borelsche Funktionen, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 651-653.
|
| Kanovei V., Koepke P., Reduzible Mengen und Differenzenketten, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 668-674. |
| Kanovei V., Koepke P., Suslinmengen, Indizes, Trennbarkeit, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 703-714. |
| Kanovei V., Koepke P., Varia, Kommentare,
In: Felix Hausdorff,
Gesammelte Werke. Band III: Descriptive Mengenlehre und Topologie,
Berlin: Springer, 2008, pp. 732-737. |
| Kanovei V., A dichotomy below E_1 * E_3,
Advances in set-theoretic topology, International conference, June 9-19, 2008,
Abstracts,
International Centre for Scientific Culture, Erice, Italy, 2008.
http://www.math.sci.ehime-u.ac.jp/erice/ |
| Friedman S.D., Kanovei V., Some natural equivalence relations in the Solovay model,
Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg,
2008, 78, 1, pp. 91--98. http://dx.doi.org/10.1007/s12188-008-0003-y |
| Kanovei V., Reeken Michael, Development in nonstandard set theoretic analysis,
Scientiae Mathematicae Japonicae,
2008, 68, 1, pp. 141--176. http://www.jams.or.jp/notice/scmj/68-1.html |
| Kanovei V., Uspensky V.A., Linton Tom, Lebesgue measure and gambling.
Sb. Math., 2008, 199, 11, pp. 1597--1619.
http://iitp.ru/www.mathnet.ru/sm3948 |
| Gorbunov K., Kanovei V., Lyubetsky V., “Inferring optimal scenario of gene evolution along a species tree”
Abstracts of The Sixth International Conference on Bioinformatics of Genome Regulation and Structure (BGRS’2008), Novosibirsk, June 22–28, p. 90. http://www.bionet.nsc.ru/meeting/bgrs2008/BGRS2008_Proceedings.pdf |
| Friedman Sy-D., Kanovei V., Lyubetsky V., On ROD reducibility of equivalence relations in Solovay model,
Methods of Logic in Mathematics V,
Russian Academy of Sciences, Steklov Institute of Mathematics and Euler International Mathematical Institute, Proceedings of International Conference, St. Petersburg, Russia, June 1-7 2008, p. 6. |
| Kanovei V., Lyubetsky V., Borel reducibility as an additive property of domains,
Journal of Mathematical Sciences,
2009, 158, 5, pp. 708–712.
https://link.springer.com/article/10.1007/s10958-009-9406-2 http://www.mathnet.ru/php/getFT.phtml?jrnid=znsl&paperid=2151&what=fullt&option_lang=rus |
| Kanovei V., Borel equivalence relations: structure and classification,
University Lectures series of the AMS, 2008. Monograph ISBN: 978-0-8218-4453-3
http://www.ams.org/bookstore-getitem/item=ulect-44 |
2007 |
| Kanovei V., A weak dichotomy below E_1 x E_3.
arXiv:0707.2706 [math.LO].
Wed, 18 Jul 2007. http://arxiv.org/abs/0707.2706 |
| Kanovei V., Canonization of Borel equivalence relations on large sets.
Euler and modern combinatorics, international conference. June 1-7, 2007.
Program, abstracts, pp. 12-13.
Euler International Mathematical Institute,
St.Petersburg, 2007.
|
| Kanovei V., Lyubetsky V., Contemporary Set Theory: foundations of descriptive dynamics.
(Russian.), Nauka, 2007. Monograph ISBN: 978-5-02-035577-4 http://www.ozon.ru/context/detail/id/3938505/ |
| Kanovei V., Lyubetsky V., Problems of set-theoretic non-standard analysis,
Russian Mathematical Surveys, 2007, 62(1), pp. 45–111. http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=5588&what=fullt&option_lang=rus |
| Kanovei V., Lyubetsky V., Reeken M., On reducibility of monadic equivalence relations,
Math. Notes, 2007, V. 81, No 6, pp. 757–766. http://www.mathnet.ru/links/4511ac41dc80f2435c1b79658aa17116/mzm3735.pdf |
2006 |
| Kanovei V., Lyubetsky V., A cofinal family of equivalence relations and Borel ideals generating them.
Proc. Moscow Steklov Inst. Math., 2006, 252, pp. 85--103. http://mi.mathnet.ru/tm65 |
| Kanovei V., Uspensky V.A., Uniqueness of nonstandard extensions.
Moscow Univ. Math. Bull., 2006, 61, 5, pp. 1--8
http://elibrary.ru/item.asp?id=9297010 |
| Kanovei V., Reeken M., Effective cardinals in the nonstandard universe.
Mathematical Logic in Asia.
Proceedings of the 9th Asian Logic Conference.
Novosibirsk, Russia, 16--19 August, 2005, pp. 113--144.
World Scientific Publishers, 2006.
http://iitp.ru/https://www.worldscientific.com/worldscibooks/10.1142/6255 |
2005 |
| Kanovei V., Lyubetsky V., Perfect subsets of invariant CA-sets.
Math.Notes, 2005, 77, 3, pp. 307--310. http://mi.mathnet.ru/mz2496 |
| Kanovei V., Uspensky V.A., On the equivalence of two forms of the continuum hypothesis.
Moscow Univ. Math. Bull., 2005, 3, pp. 45--46 http://elibrary.ru/item.asp?id=9133206 |
| Kanovei V., Lyubetsky V., A cofinal family of equivalence relations generated by Borel ideals.
Logic Colloquium 2005.
ASL European Summer meeting. July 28 -- August 3,
Athens, Greece, pp. 83.
Department of Mathematics, University of Athens, Greece, 2005.
|
2004 |
| Kanovei V., Shelah S., A definable nonstandard model of the reals.
J. Symbolic Logic, 2004, 69, 1, pp. 159--164.
http://www.jstor.org/discover/10.2307/30041716?uid=2129&uid=2&uid=70&uid=4&sid=21102182105633 |
| Kanovei V., Reeken M., Borel irreducibility between two large families of Borel equivalence relations.
Logic Colloquium 99,
Lecture Notes in Logic, 17.
Association for Symbolic Logic, 2004, pp. 100--110. http://iitp.ru/https://aslonline.org/books/lecture-notes-in-logic/available-volumes/lecture-notes-in-logic-17/ |
| Kanovei V., Reeken M., Shelah S., Fully saturated extensions of the standard universe.
Logic, algebra and geometry, June 1 -- 7, 2004,
program, abstracts, St.,Petersburg, pp. 16--17.
Euler International mathematical institute,
St. Petersburg, 2004. |
| Kanovei V., Reeken M., Shelah S., Fully saturated extensions of the standard universe.
Models of Arithmetic and Analysis,
International Congress, Pisa, June 25-26, 2004,
Program and abstracts, pp. 1.
Pisa, Italy, 2004. http://www.dm.unipi.it/~dinasso/marian2004/kanovei.pdf |
| Kanovei V., Reeken M., Shelah S., Fully saturated extensions of standard universe.
Timetable and abstracts, Logic Colloquium 2004,
p. 117. Torino, Italy, 2004. |
| Kanovei V., Reeken Michael, Nonstandard analysis, axiomatically.
Series: Springer Monographs in Mathematics
2004, XVI, 408 p., Monograph
ISBN: 978-3-540-22243-9
http://www.springer.com/math/analysis/book/978-3-540-22243-9 |
| Kanovei V., Lyubetsky V., On the set of constructive real numbers,
Proceedings of the Steklov Mathematical Institute,
V. 247, 2004, pp. 83–114. http://mi.mathnet.ru/tm12 |
2003 |
| Kanovei V., Reeken M., Some new results on Borel irreducibility of equivalence relations.
Izvestiya: Mathematics, 2003, 67, 1, pp. 55--76. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=418&option_lang=rus |
| Kanovei V., Lyubetsky V., On some classical problems of descriptive set theory.
Russian Math. Surveys, 2003, 58, 5, pp. 839--927. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=666&option_lang=rus |
| Kanovei V., Reeken M., A theorem on ROD-hypersmooth equivalence relations
in the Solovay model.
Math. Logic Quarterly, 2003, 49, 3, pp. 299--304.
http://onlinelibrary.wiley.com/doi/10.1002/malq.200310030/abstract |
| Kanovei V., Reeken M., Borel and countably determined
reducibility in nonstandard domain.
Monatshefte fur Mathematik, 2003, 140, 3, pp. 197--231.
doi: 10.1007/s00605-003-0004-y
http://link.springer.com/content/pdf/10.1007%2Fs00605-003-0004-y.pdf |
| Durand B., Kanovei V., Uspensky V.A., Vereshchagin N., Do stronger definitions of randomness exist?
Theor. Comput. Sci., 2003, 290, 3, pp. 1987--1996
http://www.sciencedirect.com/science/article/pii/S0304397502000403 |
2002 |
| Brieskorn E., Chatterji S.D., Epple M., Felgner U., Herrlich H., Husek M., Kanovei V., et al., editors ., Felix Hausdorff.
Gesammelte Werke, Band II: Grundzuege der Mengenlehre.
Berlin: Springer, 2002, xviii+883 pp.,
Monograph ISBN: 3-540-42224-2.
http://iitp.ru/https://books.google.ru/books/about/Felix_Hausdorff_Gesammelte_Werke_Band_II.html?id=3nth_p-6DpcC&re |
| Brieskorn E., Chatterji S.D., Epple M., Felgner U., Herrlich H., Husek M., Kanovei V., et al., Anmerkungen der Herausgeber.
In: Felix Hausdorf,
Gesammelte Werke, Band II: Grundzuege der Mengenlehre,
Berlin: Springer, 2002, pp. 577--617. |
| Kanovei V., Koepke P., Deskriptive Mengenlehre in Hausdorffs Grundzuegen der Mengenlehre.
In: Felix Hausdorf,
Gesammelte Werke, Band II:
Grundzuege der Mengenlehre, Springer, 2002, pp. 773--787. http://www.amazon.com/Felix-Hausdorff-Gesammelte-Grundz%C3%BCge-Mengenlehre/dp/3540422242 |
2001 |
| Kanovei V., Reeken M., On Ulam stability of the real line.
Unsolved Problems in Mathematics for the 21th Century: A Tribute to Kioshi Iseki"s 80th Birthday,
IOS Press, Amsterdam, 2001, pp. 169--181.
http://books.google.ru/books?id=yHzfbqtVGLIC&pg=PA169&lpg=PA169&dq=Kanovei+On+Ulam+stability+of+the+ |
| Christensen J.R.P., Kanovei V., Reeken M., On Borel orderable groups.
Topology and its Applications, 2001, 109, pp. 285--299.
http://www.sciencedirect.com/science/article/pii/S0166864199001649 |
| Kanovei V., Reeken M., Nonstandard set theory in e-language.
Math. Notes, 2001, 70, 1, pp. 42--45. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=717&option_lang=rus |
| Kanovei V., A version of the Jensen -- Johnsbraten coding at arbitrary level n>3.
Archive for Math. Logic, 2001, 40, 8, pp. 615--628.
http://link.springer.com/article/10.1007/s001530100087 |
2000 |
| Kanovei V., Linearization of definable order relations.
Annals of Pure and Applied Logic, 2000, 102, 1--2, pp. 69--100. http://www.sciencedirect.com/science/article/pii/S0168007299000135 |
| Kanovei V., Reeken M., Extending standard models of ZFC to models of nonstandard set theories.
Studia Logica, 2000, 64, pp. 37--59. http://link.springer.com/article/10.1023%2FA%3A1005286212737 |
| Kanovei V., Reeken M., On Baire measurable homomorphisms of quotients of the additive group of the reals.
Math. Logic Quarterly, 2000, 46, 3, pp. 377--384.
http://onlinelibrary.wiley.com/doi/10.1002/1521-3870(200008)46:3<377::AID-MALQ377>3.0.CO;2-9/abstrac |
| Kanovei V., Reeken M., A nonstandard set theory in the e-language.
Archive for Math. Logic, 2000, 39, 4, pp. 403--416. http://link.springer.com/article/10.1007%2Fs001530050155 |
| Kanovei V., Reeken M., On Ulam"s problem of stability of non-exact homomorphisms.
Proc. Moscow Steklov Inst. Math., 2000, 231, pp. 238--270.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tm&paperid=518&option_lang=rus |
| Kanovei V., Reeken M., New Radon-Nikodym ideals.
Mathematika, 2000, 47, no. 1--2, pp. 219--227.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7015000 |
1999 |
| Kanovei V., Non-wellfounded iterations of perfect set forcing.
J. Symbolic Logic, 1999, 64, 2, pp. 551--574. http://www.jstor.org/discover/10.2307/2586484?uid=2129&uid=2&uid=70&uid=4&sid=21102181989303 |
| Kanovei V., Reeken M., A nonstandard proof of the Jordan curve theorem.
Real Analysis Exchange, 1999, 24, 1, pp. 161--170. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rae/1300906020 |
| Kanovei V., Reeken M., Special model axiom in nonstandard set theory.
Math. Logic Quarterly, 1999, 45, 3, pp. 371--384 http://onlinelibrary.wiley.com/doi/10.1002/malq.19990450308/abstract |
| Kanovei V., Reeken M., Extension of standard models of ZFC to models of nonstandard Nelson"s set theory IST.
Math. Notes, 1999, 66, 2, pp. 160--166. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=1157&option_lang=rus |
1998 |
| Kanovei V., When a partial Borel order is Borel linearizable.
Fundamenta Mathematicae, 1998, 155, 3, pp. 301--309.
http://iitp.ru/https://eudml.org/doc/212258 |
| Kanovei V., Reeken M., Elementary extensions of external classes in a nonstandard universe.
Studia Logica, 1998, 60, 2, pp. 253--273. http://link.springer.com/article/10.1023%2FA%3A1005064032270 |
| Kanovei V., Zapletal J., Pyramidal structure of constructibility degrees.
Math. Notes, 1998, 63, 4, pp. 556--559. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=1325&option_lang=rus |
| Kanovei V., Ulm classification of analytic equivalence relations in generic universes.
Math. Logic Quarterly, 1998, 44, 3, pp. 287--303. http://onlinelibrary.wiley.com/doi/10.1002/malq.19980440302/abstract |
| Kanovei V., On ``star"" schemata of Kossak and Paris,
Logic Colloquium "96,
Lecture Notes in Logic 12, Springer, 1998, pp. 101--114. http://link.springer.com/chapter/10.1007%2F978-3-662-22110-5_4 |
1997 |
| Kanovei V., Reeken M., Mathematics in a nonstandard world, I.
Math. Japonica, 1997, vol. 45, 2, pp. 369--408.
http://www.jams.or.jp/notice/mj/45-2.html |
| Kanovei V., Reeken M., Mathematics in a nonstandard world, II.
Math. Japonica, 1997, vol. 45, 3, pp. 555--571.
http://www.jams.or.jp/notice/mj/45-3.html |
| Kanovei V., Non--Glimm--Effros equivalence relations at second projective level.
Fundamenta Mathematicae, 1997, 154, 1, pp. 1--35.
http://iitp.ru/https://eudml.org/doc/212225 |
| Kanovei V., van Lambalgen M., On a Spector ultrapower of Solovay model.
Math. Logic Quarterly, 1997, 43, 2, pp. 389--395.
http://onlinelibrary.wiley.com/doi/10.1002/malq.19970430311/abstract |
| Kanovei V., Two dichotomy theorems on colourability of non-analytic graphs.
Fundamenta Mathematicae, 1997, 154, 2, pp. 183--201.
http://iitp.ru/https://eudml.org/doc/212233 |
| Kanovei V., Reeken M., Isomorphism property in nonstandard extensions of the ZFC universe.
Annals of Pure and Applied Logic, 1997, 88, pp. 1--25. http://www.sciencedirect.com/science/article/pii/S0168007297000110 |
| Kanovei V., An Ulm--type classification theorem for equivalence relations in Solovay model.
J. Symbolic Logic, 1997, 62, 4, pp. 1333--1351. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jsl/1183745385 |
1996 |
| Kanovei V., Reeken M., Loeb measure from the point of view of coin flipping game.
Math. Logic Quarterly, 1996, 42, 1, pp. 19--26.
http://dx.doi.org/10.1002/malq.19960420103 |
| Kanovei V., Reeken M., Internal approach to external sets and universes. 3. Partially saturated universes.
Studia Logica, 1996, 56, 3, pp. 293--322.
http://link.springer.com/article/10.1007%2FBF00372770 |
| Kanovei V., On external Scott algebras in nonstandard models of Peano arithmetic.
J. Symbolic Logic, 1996, 61, 2, pp. 586--608. http://www.jstor.org/discover/10.2307/2275677?uid=2129&uid=2&uid=70&uid=4&sid=21102182737583 |
| Kanovei V., Reeken M., Summation of divergent series from the nonstandard point of view.
Real Analysis Exchange, 1996, 21, 2, pp. 453--477. http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.rae/1339694079&page |
| Kanovei V., Topologies generated by effectively Suslin sets
and their applications in descriptive set theory.
Russian Math. Surveys, 1996, 51, No.3, pp. 385--417. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=968&option_lang=rus |
1995 |
| Kanovei V., Uniqueness, collection, and external collapse of cardinals in IST and models of Peano arithmetic.
J. Symbolic Logic, 1995, 60, 1, pp. 318--324.
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jsl/1183744692 |
| Kanovei V., Reeken M., Internal approach to external sets and universes. 1. Bounded set theory.
Studia Logica, 1995, 55, 2, pp. 229--257. http://link.springer.com/article/10.1007%2FBF01061236 |
| Kanovei V., Reeken M., Internal approach to external sets and universes. 2. External universes over the BST universe.
Studia Logica, 1995, 55, 3, pp. 347--376. http://link.springer.com/article/10.1007%2FBF01057803 |
1994 |
| Kanovei V., A course on Foundations of Nonstandard Analysis,
IPM Lecture Notes Series 1, 1994, 149 pp. Monograph
http://math.ipm.ac.ir/publications/pic_books/course_large.jpg |
1992 |
| Kanovei V., On the extension principle in internal set theory.
Siberian Math. J., 1992, 33, 6, pp. 999--1010. http://mi.mathnet.ru/smj1717 |
1991 |
| Kanovei V., The cardinality of the set of Vitali equivalence classes.
Math. Notes, 1991, 49, 4, pp. 370--374. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=2934&option_lang=rus |
| Kanovei V., Undecidable hypotheses in Edward Nelson"s internal set theory.
Russian Math. Surveys,1991, 46: 6, pp. 1--54 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=4674&option_lang=rus |
1990 |
| Kanovei V., Bounded sets in Edvard Nelson"s internal set theory.
Nonstandard analysis. 3rd USSR seminar. Saratov, 1990, pp. 15--23. |
1989 |
| Kanovei V., On separability of external sets.
Mathematical conference dedicated to the memory of M. Ya. Suslin,
Saratov, 1989, pp. 38--45. |
1988 |
| Kanovei V., The correctness of Euler"s method for the factorization of the sine function into an infinite product.
Russian Math. Surveys, 1988, 43, 4, pp. 65--94. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=1834&option_lang=rus |
| Kanovei V., Kolmogorov"s ideas in the theory of operations on sets.
Russian Math. Surveys, 1988, 43, 6, pp. 111--155. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=2048&option_lang=rus |
| Kanovei V., Uspensky V.A., M.Ya.Souslin"s contribution to set-theoretic mathematics.
Moscow Univ. Math. Bull., 1988, 43, 5, pp. 29--40. http://iitp.ru/https://istina.msu.ru/publications/article/93856823/ |
| Grishin V., Kanovei V., On work in descriptive set theory carried out at the Mathematical Institute of the Academy of Sciences.
Proc. Steklov Inst. Math., 1990, Issue 1, pp. 245--265. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tm&paperid=1926&option_lang=rus |
1987 |
| Kanovei V., N.N.Luzin"s problems on the existence of CA sets without perfect subsets.
Math. Notes, 1987, 41, pp. 422--426. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=4915&option_lang=rus |
| Kanovei V., ``Nonstandard"" construction of power series.
In: V. A. Uspensky, What is the nonstandard analysis, M.: Nauka, 1987, pp. 121--124.
|
1985 |
| Kanovei V., Some problems of descriptive set theory and type theory.
Abstract of D.Sc. thesis in physics and mathematics.
ÌÈÀÍ èì. Â.À.Ñòåêëîâà, 1985, 18 ñ. http://lpcs.math.msu.su/~zolin/phd/#1985 |
| Kanovei V., Problem of the existence of nonborel AF_II sets.
Math. Notes, 1985, 37, pp. 156--161 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=5305&option_lang=rus |
| Kanovei V., Development of descriptive set theory under the influence of N.N.Luzin"s work.
Russian Math. Surveys, 1985, 40, 3, pp. 135--180. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=2649&option_lang=rus |
| Kanovei V., The axiom of determinacy and the modern development of descriptive set theory.
J. Soviet Math., 1988, 40, 3, pp. 257--287. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=inta&paperid=109&option_lang=rus |
1984 |
| Uspensky V.A., Kanovei V., N.N. Luzin, an outstanding mathematician and teacher.
Vestnik Akademii Nauk SSSR, 1984, 11, pp. 95--102. (Russian.) |
| Kanovei V., Undecidable and decidable properties of constituents.
Math. USSR Sbornik, 1985, 52, 2, pp. 491--519. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=2064&option_lang=rus |
| Kanovei V., The axiom of choice and the axiom of determinateness. Moscow, Nauka, 1984, 63 pp.
Monograph http://iitp.ru/https://zbmath.org/?q=an%3A0599.03053 |
1983 |
| Kanovei V., Some problems of descriptive set theory and definability in the theory of types.
Studies in nonclassical logic and formal systems,
work collect.,
Moscow, 1983, pp. 21--81 |
| Kanovei V., The structure of constituents of CA sets.
Siberian Math. J., 1983, 24, 2, pp. 198--215. |
| Kanovei V., Generalization of P.S.Novikov"s theorem on the crossections of Borel sets.
Math. Notes, 1983, 33, 2, pp. 144--146 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=5681&option_lang=rus |
| Kanovei V., An answer on N. N. Luzin"s question about the separability of CA curves.
Math. Notes, 1983, 33, 3, pp. 223--224. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=10095&option_lang=rus |
| Kanovei V., Uspensky V.A., Luzin"s problems on constituents and their fate.
Moscow Univ. Math. Bull.
1983, 38, 6, pp. 86--102 http://iitp.ru/https://istina.msu.ru/publications/article/93856782/ |
1982 |
| Kanovei V., On N.N. Luzin"s problems on the embeddability and decomposability of projective sets.
Math. Notes, 1982, 32, pp. 494--499. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=6055&option_lang=rus |
| Kanovei V., Projective hierarchy of N.N. Luzin: the current state of the theory.
Appendix to the Russian translation of
Handbook of Mathematical Logic, part 2: Set Theory, Moscow, Nauka,1982,
pp. 273--364. |
1981 |
| Kanovei V., On uncountable sequences of sets given by the sieve operation,
Soviet Math. Dokl., 1981, 23, 2, pp. 352--356. http://mi.mathnet.ru/dan44352 |
| Kanovei V., Ostrovsky A.V., On non-Borel F_II sets,
Soviet Math. Dokl., 1981, 24, 2, pp. 386--389. http://mi.mathnet.ru/dan44783 |
| Kanovei V., Theory of Zermelo without the power set axiom and the theory of Zermelo -- Fraenkel without the power set axiom are relatively
consistent,
Math. Notes, 1981, 30, 3, pp. 695--702. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=6204&option_lang=rus |
1980 |
| Kanovei V., On some problems of descriptive set theory and the connection between constructibility and definability.
Soviet Math. Dokl., 1980, 22, 1, pp. 163 - 167. http://mi.mathnet.ru/dan43771 |
1979 |
| Kanovei V., On the definability of forcing in analysis.
Moscow Univ. Math. Bull, 1979, 34, 2, pp. 3--13. |
| Kanovei V., On descriptive forms of the countable axiom of choice.
Studies in nonclassical logic and set theory, work collect., Moscow, 1979, pp. 3--136. |
| Kanovei V., The set of all analytically definable sets of natural numbers can be defined analytically.
Math. USSR Izv., 1980, 15, pp. 469--500.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=1755&option_lang=rus |
| Kanovei V., A consequence of the Martin Axiom.
Math. Notes, 1980, 26, pp. 549--553.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=8384&option_lang=rus |
1978 |
| Kanovei V., The significance of the parameters and of the complexity of the basic formula in the comprehension schema for second order
arithmetic.
Soviet Math. Dokl. 1978, 19, pp. 1556--1559.
http://mi.mathnet.ru/dan42219 |
| Kanovei V., Proof of a theorem of N.N. Luzin.
Math. Notes, 1978, 23, pp. 35--37.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=8119&option_lang=rus |
| Kanovei V., The optimal strategy of distribution of resources in planning of railroad cargo transportation.
Collected works of high school, 597,
Moscow Transport Engineering Institute, 1978, pp. 86--107. |
| Kanovei V., On the nonemptiness of classes in axiomatic set theory.
Math USSR Izv., 1978, 12, pp. 507--535.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=1779&option_lang=rus |
1976 |
| Kanovei V., Definability using the degrees of constructibility.
Studies in set theory and non-classical logic, work collect.,
M., Nauka, 1976, pp. 5--95.
http://www.logic-books.info/node/383 |
| Kanovei V., Consistency of some propositiona of descriptive set theory which express the existence of objects with paradoxical properties.
Abstract of Ph.D. thesis in physics and mathematics,
ÌÃÓ, 1976, 16 ñ.
http://iitp.ru/https://search.rsl.ru/ru/record/01006983244 |
1975 |
| Kanovei V., The majorization of initial segments of degrees of constructibility.
Math. Notes, 1975, 5--6, pp. 563--567.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=7614&option_lang=rus |
| Kanovei V., The independence of some propositions of descriptive set theory and second order arithmetic.
Soviet Math. Dokl, 1975, 16, 4, pp. 937--940. http://mi.mathnet.ru/dan39167 |
1974 |
| Kanovei V., On degrees of constructibility and descriptive properties of the set of real numbers in the initial model and in its extensions.
Soviet Math. Dokl, 1974, 15, 3, pp. 866--868.
http://mi.mathnet.ru/dan38331 |
1973 |
| Kanovei V., The problem of singular cardinals.
Math. Notes, 1973, 13, pp. 429--433. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=7176&option_lang=rus |