Cauchy"s work on integral geometry, centers of curvature, and other applications of infinitesimals.
Real Analysis Exchange, 2020, to appear.

Canonization of smooth equivalence relations on infinite-dimensional E0-large products.
Notre Dame J. Form. Logic, 2020, to appear.
SCIMAGO, Q2.

Definable selector for $\Delta^0_2$ 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.
Izvestiya: Mathematics, 2019.
Submitted.
WoS Q2

Models of set theory in which separation theorem fails.
arXiv:1905.11241 [math.LO], May 2019.
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Definable Hamel bases and ACω(R).
Fundamenta Mathematicae. Submitted.
SCOPUS, Q2

Absoluteness of the Solovay set Σ.
Siberian Mathematical Journal, 2019, 60, no 6, pp. 1003-1006.
DOI: 10.1134/S0037446619060089
SCIMAGO, Q2
WoS Q3

Factoring Solovay-random extensions, with application to the Reduction property.
Monatshefte fur Mathematik, 2019, submitted.
WoS Q2

The full basis theorem does not imply analytic wellordering,
Annals of pure and applied logic, 2019, submitted.
WoS Q1

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 by Journal Citation Reports JCR and SCImago SJR.)
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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
SCOPUS, Q2
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Definable elements of definable Borel sets.
Mathematical Notes, 2019, 105, no 5, pp. 684-693.
DOI: 10.1134/S0001434619050055
SCIMAGO, Q2
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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
SCIMAGO Q1
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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 Q1
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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:1810.12542 [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
WoS Q3
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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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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:1712.00769 [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:1702.03566 [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 [SCIMAGO, Q2]
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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, Sep 2017, Vol. 102, Iss. 3–4, P. 338–349. doi:10.1134/S0001434617090048 [SCIMAGO, Q2]
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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
WoS Q3
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A generic property of Solovay"s set Σ.
arXiv:1611.00176 [math.LO], pp. 1-4, November 2016.
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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.
September 2016, arXiv:1609.01032 [math.LO], pp. 1-12.
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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 $Pi^1_2$ uniformization and $Pi^1_3$ 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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