Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes, Russian Mathematics, Izvestiya, 2018, vol. 82, to appear.
Go to publication

Definable E0 classes at arbitrary projective levels. May 2017, arXiv:1705.02975 [math.LO], pp. 1--26. Submitted to Annals of pure and applied logic.
Go to publication

Cauchy"s infinitesimals, his sum theorem, and foundational paradigms. Foundations of Science, 2017, accepted.
Go to publication

The full basis theorem does not imply analytic wellordering. February 2017, arXiv:1702.03566 [math.LO], pp. 1-63.
Go to publication

Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 2017, accepted.

Countable OD sets of reals belong to the ground model, Archive for Mathematical Logic, 2017, to appear.

A positive function with vanishing Lebesgue integral in ZF. Real Analysis Exchange, 2017, 42, no. 2, to appear.

Gregory"s sixth operation, Foundations of Science, 2017. First Online 20 December 2016, DOI: 10.1007/s10699-016-9498-3
Go to publication

Minimally definable hyperreals with transfer, Journal of symbolic logic, 2017, to appear.

Interpreting the infinitesimal mathematics of Leibniz and Euler, Journal of General Philosophy of Science, 2017, 48, issue 2, pp, 195--238. DOI: 10.1007/s10838-016-9334-z
Go to publication

A definable countable set not containing definable elements, Mathematical notes, 2017, submitted.

Controversies on foundations of analysis: comments on Schubring’s conflicts. Foundations of Science, 2017, 22, 1, pp. 125--140.
Go to publication

A Groszek – Laver pair of undistinguishable E₀ classes. Mathematical Logic Quarterly, 2017, 63, No. 1–2, pp. 19–31. doi: 10.1002/malq.201500020.
Go to publication

A generic property of Solovay"s set Σ. November 2016, arXiv:1611.00176 [math.LO], pp. 1-4.
Go to publication

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.
Go to publication

Countable OD sets of reals belong to the ground model. September 2016, arXiv:1609.01032 [math.LO], pp. 1-12.
Go to publication

A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos. Logica Universalis, 2016, 10, pp. 393-405.
Go to publication

Toward a history of mathematics focused on procedures, Foundations Of Science, 2016, First Online 21 September 2016, DOI: 10.1007/s10699-016-9498-3
Go to publication

Small oscillations of the pendulum, Euler’s method, and adequality, Quantum Studies: Mathematics and Foundations, 2016, 3, no 3, pp 231–236
Go to publication

OD elements of countable OD sets in the Solovay model. March 2016, arXiv:1603.04237 [math.LO], pp. 1-20.
Go to publication

Is Leibnizian calculus embeddable in first order logic? Foundations of Science, First Online: 22 June 2016, DOI: 10.1007/s10699-016-9495-6
Go to publication

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
Go to publication

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.
Go to publication

On countable cofinality and decomposition of definable thin orderings. Fundamenta mathematicae, 2016, 235, no 1, pp. 13-36.
Go to publication

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.
Go to publication

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.
Go to publication

“Grossone approach to Hutton and Euler transforms” Applied Mathematics and Computation, 2015, 255, pp. 36–43.
Go to publication

Euler"s lute and Edward"s oud. Mathematical Intelligencer, 2015, 37, 4, pp. 48--51.
Go to publication

A definable $E_0$ class containing no definable elements, Archive for Mathematical Logic, 2015, 54, 5, pp. 711--723.
Go to publication

Generalization of one construction by Solovay, Siberian Mathematical Journal, 2015, 56, no. 6, pp. 1072–1079

Proofs and retributions, Foundations of Science, 2015, 20, 1, pp 1-25.
Go to publication

On effective σ-boundedness and σ-compactness in Solovay"s model, Mathematical notes, 2015, 98, 1-2, pp. 273--282.
Go to publication

On countable cofinality and decomposition of definable thin orderings, arXiv:1412.0195 [math.LO], Dec. 2014, 21 p.
Go to publication

Counterexamples to countable-section Π12 uniformization and Π13 separation, arXiv:1410.2537 [math.LO], Oct. 2014, 18 p.
Go to publication

A definable $E_0$-class containing no definable elements, arXiv:1408.6642 [math.LO], Aug 2014, 12 p.
Go to publication

A countable definable set of reals containing no definable elements, arXiv:1408.3901 [math.LO], Aug. 2014, 11 p.
Go to publication

Linearization of partial quasi-orderings in the Solovay model revisited, arXiv:1408.1202 [math.LO], Aug. 2014, 13 p.
Go to publication

Bounding and decomposing thin analytic partial orderings, arXiv:1407.0929v2 [math.LO], Jul 2014, 12 p.
Go to publication

A generalization of Solovay"s Sigma-construction. arXiv:1402.0961 [math.LO]. 5 Feb 2014, 6 p.
Go to publication

On the automorphisms behind the Gitik -- Koepke model. In: Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch. College publications, London, 2014, SeriesTributes, Vol. 23, pp. 229--253
Go to publication

Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow. Notices of the AMS, 2014, 61, 8, pp. 848--864.
Go to publication

On countable cofinality of definable chains in Borel partial orders. arXiv:1312.2064 [math.LO]. Sat, 7 Dec 2013
Go to publication

Surreal numbers from the point of view of nonstandard analysis, Sy David Friedman"s 60th-Birthday Conference, Vienna, Austria, July 2013.
Go to publication

Felix Hausdorff. Gesammelte Werke, Band IA: Allgemeine Mengenlehre. Berlin: Springer, 2013, xxvi+538 pp., Monograph ISBN: 978-3-642-25598-4.
Go to publication

Is mathematical history written by the victors? Notices of the AMS, 2013, 60, no 7, pp. 886-904.
Go to publication

Canonical Ramsey Theory on Polish Spaces. Cambridge University Press, Cambridge, UK, 2013, viii+269 pp., Monograph ISBN 978-1-107-02685-8
Go to publication

Contemporary Set Theory: absolutely undecidable classical problems. (Russian.) Monograph, published by Independent Moscow university, 2013, 384 pages.
Go to publication

Kommentar zu [H 1936b], Summen von $aleph_1$ Mengen. In: Felix Hausdorff, Gesammelte Werke. Band Ia: Allgemeine Mengenlehre, Berlin: Springer, 2013, pp. 364-366.
Go to publication

Kommentar zu [H 1909a], Die Graduierung nach dem Endverlauf. In: Felix Hausdorff, Gesammelte Werke. Band Ia: Allgemeine Mengenlehre, Berlin: Springer, 2013, pp. 336-346.
Go to publication