An unpublished theorem of Solovay, revisited.
Journal of Mathematical Logic, 2020. Online first.
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, to appear.
DOI: 10.1070/IM8937
WoS Q2
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Definable Hamel bases and AC_ω(R).
Fundamenta Mathematicae, 2021, to appear.
WoS Q3
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Factoring Solovay-random extensions, with application to the Reduction property.
Monatshefte fur Mathematik, 2020. Online first.
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, to appear. (WoS Q1)

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
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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
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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
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Definable elements of definable Borel sets. Mathematical Notes, 2019, 105, no 5, pp. 684-693. DOI: 10.1134/S0001434619050055
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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
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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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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.
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A countable definable set of reals containing no definable elements, arXiv:1408.3901v2 [math.LO], Sept. 2018, 11 p.
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A model of second-order arithmetic satisfying AC but not DC.
arXiv:1808.04732 [math.LO], August 2018.
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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)
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Canonization of smooth equivalence relations on infinite-dimensional perfect cubes. arXiv:1804.05174 [math.LO], April 2018.
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Monotone subsequence via ultrapower.
Open Mathematics, 2018, 16, 1, c. 149-153
DOI: 10.1515/math-2018-0015
WoS Q2
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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
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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
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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
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Gregory"s sixth operation,
Foundations of Science, 2018, 23, 1, pp. 133--144.
DOI: 10.1007/s10699-016-9512-9
WoS Q2
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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)
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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)
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Minimal axiomatic frameworks for definable hyperreals with transfer. arXiv:1707.00202 [math.LO], July 2017.
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Cauchy, infinitesimals and ghosts of departed quantifiers,
Mat. Stud. 2017, 47, 2, 115--144
doi:10.15330/ms.47.2.115-144
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Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v1 [math.LO], December 2017.
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Definable minimal collapse functions at arbitrary projective levels. arXiv:1707.07320 [math.LO], July 2017.
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Definable E₀ classes at arbitrary projective levels. arXiv:1705.02975 [math.LO], May 2017.
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The full basis theorem does not imply analytic wellordering. arXiv:1702.03566v2 [math.LO], February 2017.
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A generic property of the Solovay set Σ. Siberian Mathematical Journal, 2017, Vol. 58, Iss. 6, P. 1012–1014. doi:10.1134/S0037446617060106
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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
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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
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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
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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
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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
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