Jensen Reals by Means of Second-Order Peano Arithmetic.
Axioms, 2024, 13(2), Article no 96.
DOI: 10.3390/axioms13020096 (WoS Q2) Go to publicationDownload (248.3 KB)

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
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Parameterfree Comprehension does not imply full Comprehension in second order Peano arithmetic.
Studia Logica,
2024, accepted.
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2023 year

Authors: 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
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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
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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 .
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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
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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)
Go to publication

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 Go to publication

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.
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The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic. arXiv: 2209.07599 [math.LO], September 2022. Go to publication

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
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A model in which the Separation principle holds for a given effective projective Sigma-class.
arXiv: 2204.03915 [math.LO], April 2022. Go to publication

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
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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
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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
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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.
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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. Go to publication

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).
Go to publication

On effectively indiscernible projective sets and the Leibniz-Mycielski axiom.
Mathematics, 2021, Vol. 9, No. 14, Art. 1670.
DOI: 10.3390/math9141670
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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. Go to publication

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
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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
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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
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On the "definability of definable" problem of Alfred Tarski.
Mathematics, 2020, Vol. 8, No. 12, Art. 2214.
DOI: 10.3390/math8122214
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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
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Metric completions, Heine-Borel, and approachability.
Open Mathematics, 2020, Volume 18, Issue 1, 162-166.
DOI: 10.1515/math-2020-0017
WoS Q3 Go to publication

2020 year

Authors: 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 Go to publication

Canonization of smooth equivalence relations on infinite-dimensional E_{0}-large products.
Notre Dame Journal of Formal Logic,
2020, Vol. 61, No. 1, P. 117–128.
DOI: 10.1215/00294527-2019-0034
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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

2019 year

Authors: 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
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2019 year

Authors: 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
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Definable selector for Δ^{0}_{2} sets modulo countable.
arXiv: 1910.00926 [math.LO],
October 2019 Go to publication

2019 year

Authors: 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 Go to publication

Absoluteness of the Solovay set Σ.
Siberian Mathematical Journal,
2019, 60, no 6, pp. 1003-1006.
DOI: 10.1134/S0037446619060089
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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)
Go to publication

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
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Definable elements of definable Borel sets.
Mathematical Notes,
2019, 105, no 5, pp. 684-693.
DOI: 10.1134/S0001434619050055
(WoS Q3) Go to publication

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) Go to publication

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
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Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v3 [math.LO], January 2018. Go to publication