V. Kanovei - Publications

2017

Kanovei V., Katz M., Lobry C., Fletcher P., Hrbacek K., Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 2017, to appear.
Kanovei V., Lyubetsky V., Countable OD sets of reals belong to the ground model, Archive for Mathematical Logic, 2017, submitted
Kanovei V., Katz M., A positive function with vanishing Lebesgue integral in ZF. Mathematical Intelligencer, 2017, submitted.
Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., Kutateladze S., Nowik T., Sherry D., Schaps D., Gregory"s sixth operation, Foundations of Science, 2017, to appear
Herzberg F., Kanovei V., Katz M., Lyubetsky V., Minimally definable hyperreals with transfer, Journal of symbolic logic, 2017, submitted.
Kanovei V., Lyubetsky V., Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes, Russian Mathematics, Izvestiya, 2017, to appear.
Kanovei V., Lyubetsky V., A definable countable set not containing definable elements, Mathematical notes, 2017, submitted.
Golshani M., Kanovei V., Lyubetsky V., A Groszek -- Laver pair of undistinguishable $E_0$ classes. Mathematical Logic Quarterly, 2017, to appear. http://math.ipm.ac.ir/~golshani/Papers/A Groszek-Laver pair of undistinguishable E0 classes.pdf

2016

Kanovei V., Lyubetsky V., A generic property of Solovay"s set Σ. November 2016, arXiv:1611.00176 [math.LO], pp. 1-4. 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 216, 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. September 2016, arXiv:1609.01032 [math.LO], pp. 1-12. http://arxiv.org/abs/1609.01032
Błaszczyk P., Borovik A., Kanovei V., Katz M., Kudryk T., Kutateladze S., Sherry D., A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos. Logica Universalis, 2016, 10, pp. 393-405. http://link.springer.com/article/10.1007/s11787-016-0153-0?wt_mc=Internal.Event.1.SEM.ArticleAuthorO
Blaszczyk P., Kanovei V., Katz M., Kutateladze S., Sherry D., Toward a history of mathematics focused on procedures, Foundations Of Science, 2016, First Online 21 September 2016, DOI: 10.1007/s10699-016-9498-3 http://link.springer.com/article/10.1007/s10699-016-9498-3
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 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
Blaszczyk Piotr, Kanovei V., U. Katz Karin, G. Katz Mikhail, Kudryk Taras, Normann Thomas, Sherry David, Is Leibnizian calculus embeddable in first order logic? Foundations of Science, First Online: 22 June 2016, DOI: 10.1007/s10699-016-9495-6 http://link.springer.com/article/10.1007%2Fs10699-016-9495-6
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
Bair J., Blaszczyk P., Ely R., Henry V., Kanovei V., Katz K., Katz M., Kutateladze, et al. S., Interpreting the infinitesimal mathematics of Leibniz and Euler, Journal of General Philosophy of Science, First Online: 19 July 2016 DOI: 10.1007/s10838-016-9334-z http://link.springer.com/article/10.1007/s10838-016-9334-z
Kanovei V., Lyubetsky V., Counterexamples to countable-section $Pi^1_2$ uniformization and $Pi^1_3$ separation. Annals of Pure and Applied Logic, 2016, 167, 3, pp. 262–283. 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. 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., Schaps D., Sherry D., 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. 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
Blazczyk P., Kanovei V., Katz M., Sherry D., Controversies on foundations of analysis: comments on Schubring’s conflicts. Foundations of Science, First online: 24 December 2015 http://link.springer.com/article/10.1007/s10699-015-9473-4?wt_mc=internal.event.1.SEM.ArticleAuthorO
Kanovei V., Lyubetsky V., “Grossone approach to Hutton and Euler transforms” Applied Mathematics and Computation, 2015, 255, pp. 36–43. 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. http://dx.doi.org/10.1007/s00283-015-9565-6
Kanovei V., Lyubetsky V., A definable $E_0$ class containing no definable elements, Archive for Mathematical Logic, 2015, 54, 5, pp. 711--723. 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
Kanovei V., Katz Ê., Katz M., Schaps D., Proofs and retributions, Foundations of Science, 2015, 20, 1, pp 1-25. 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. 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://www.collegepublications.co.uk/tributes/?00023
Bascelli T., Kanovei V., Katz K., Katz M., Nowik T., Sherry D., 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. 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. 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. 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. 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.
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, Studies in constructive mathematics and mathematical logic. Part XI, Zapiski Nauchnyh Seminarov POMI, Vol. 358, St.Petersburg, POMI, 2008, pp. 189–198. 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://bookos.org/book/727242/dc8861

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://www.aslonline.org/books-lnl_17.html
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. 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.
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/abstract 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.
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.
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://math-portal.ru/problnaykitehprogr/

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

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.
Kanovei V., Ostrovsky A.V., On non-Borel F_II sets, Soviet Math. Dokl., 1981, 24, 2, pp. 386--389.
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.

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.
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.

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.

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.

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