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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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
WoS Q2
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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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A countable definable set containing no definable elements. Mathematical Notes, 2017, Vol. 102, Iss. 3–4, P. 338–349. doi:10.1134/S0001434617090048
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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
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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
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A Groszek-Laver pair of undistinguishable E₀ classes. arXiv:1601.03477 [math.LO], Jan 14 2016, 18 pp.
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A generic property of Solovay"s set Σ. arXiv:1611.00176 [math.LO], November 2016, 4 pp.
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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.
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Countable OD sets of reals belong to the ground model. arXiv:1609.01032 [math.LO], September 2016, 12 pp.
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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
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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
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OD elements of countable OD sets in the Solovay model.
March 2016, arXiv:1603.04237 [math.LO], pp. 1-20.
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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
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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)
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On countable cofinality and decomposition of definable thin orderings. Fundamenta mathematicae, 2016, 235, no 1, pp. 13-36. DOI: 10.4064/fm977-10-2015
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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
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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.
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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)
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Euler"s lute and Edward"s oud. Mathematical Intelligencer, 2015, 37, 4, pp. 48--51.
DOI: 10.1007/s00283-015-9565-6
SCIMAGO, Q2
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