On the significance of parameters and the projective level in the Choice and Collection axioms. arXiv: 2407.20098 [math.LO], August 2024, 127 pp.
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Jensen Δ¹_n reals by means of ZFC and second-order Peano arithmetic. Axioms, Jan 30 2024, Vol. 13, No. 2, Art. 96. DOI: 10.3390/axioms13020096 (WoS Q1)
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A good lightface Δ¹_n well-ordering of the reals does not imply the existence of boldface Δ¹_n-1 well-orderings. Annals of Pure and Applied Logic, Jun 2024, Vol. 175, Iss. 6, Art. 103426. DOI: 10.1016/j.apal.2024.103426 (WoS Q2)
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Parameterfree comprehension does not imply full comprehension in second order Peano arithmetic. Studia Logica, Apr 2024. DOI: 10.1007/s11225-024-10108-2 (WoS Q2)
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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 Q1)
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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 (WoS Q1)
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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 . (WoS Q1)
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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 (WoS Q1)
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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)
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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
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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.
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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)
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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.
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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)
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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 (WoS Q2)
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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 (WoS Q1)
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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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On Russell typicality in Set Theory. arXiv: 2111.07654 [math.LO], November 2021.
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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.
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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).
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On effectively indiscernible projective sets and the Leibniz-Mycielski axiom. Mathematics, 2021, Vol. 9, No. 14, Art. 1670. DOI: 10.3390/math9141670 (WoS Q1)
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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.
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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)
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Definable Hamel bases and AC_ω(R).
Fundamenta Mathematicae, 2021, 253, 3, p. 239-256.
DOI 10.4064/fm909-6-2020
WoS Q3
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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 (WoS Q2)
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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 (WoS Q1)
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An unpublished theorem of Solovay, revisited. arXiv:2001.11058 [math.LO], January 2020.
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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 (WoS Q1)
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On the Δ¹_n Problem of Harvey Friedman. Mathematics, 2020, Vol. 8, No. 9, Art. 1477. DOI: 10.3390/math8091477 (WoS Q1)
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On the equality modulo a countable set. Mathematical notes, 2020, Vol. 108, Iss. 4, P. 615–616. DOI: 10.1134/S0001434620090357
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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 (WoS Q1)
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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
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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
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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)
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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

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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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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Indiscernible pairs of countable sets of reals at a given projective level. arXiv: 1912.12962 [math.LO], December 2019.
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Definable selector for Δ⁰₂ sets modulo countable.
arXiv: 1910.00926 [math.LO], October 2019
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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
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Models of set theory in which separation theorem fails. arXiv:1905.11241 [math.LO], May 2019.
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Absoluteness of the Solovay set Σ. Siberian Mathematical Journal, 2019, 60, no 6, pp. 1003-1006. DOI: 10.1134/S0037446619060089 (WoS Q3)
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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)
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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)
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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)
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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)
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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)
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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.
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On intermediate extensions of generic extensions by a random real. arXiv:1811.10568 [math.LO], December 2018.
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