Countable OD sets of reals belong to the ground model. September 2016, arXiv:1609.01032 [math.LO], 12 pages
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Minimally definable hyperreals with transfer, JSL, submitted.

A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos. Logica Universalis, 2016, First online: 06 July 2016.
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Toward a history of mathematics focused on procedures, Foundations Of Science, 2016, First Online 21 September 2016, DOI: 10.1007/s10699-016-9498-3
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Small oscillations of the pendulum, Euler’s method, and adequality, Quantum Studies: Mathematics and Foundations, 2016, first online 05 may 2016.
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OD elements of countable OD sets in the Solovay model. March 2016, arXiv:1603.04237 [math.LO], 20 pages
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Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes, Russian Mathematics, Izvestiya, under consideration.

Is Leibnizian calculus embeddable in first order logic? Foundations of Science, 2016, vol. 21, no 2, .
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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

Interpreting the infinitesimal mathematics of Leibniz and Euler, Journal of General Philosophy of Science, 2016, First online: 19 July 2016.
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A definable countable set not containing definable elements, Mathematical notes, under consideration.

Controversies on foundations of analysis: comments on Schubring’s conflicts. Foundations of Science, 2016, to appear. First online: 24 December 2015,
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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.
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A Groszek -- Laver pair of undistinguishable $E_0$ classes. Mathematical Logic Quarterly, 2016, to appear.
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On countable cofinality and decomposition of definable thin orderings. Fundamenta mathematicae, 2016, 235, no 1, pp. 13-36.
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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.
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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.
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Euler"s lute and Edward"s oud. Mathematical Intelligencer, 2015, 37, 4, pp. 48--51.
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A definable $E_0$ class containing no definable elements, Archive for Mathematical Logic, 2015, 54, 5, pp. 711--723.
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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.
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On effective σ-boundedness and σ-compactness in Solovay"s model, Mathematical notes, 2015, 98, 1-2, pp. 273--282.
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On countable cofinality and decomposition of definable thin orderings, arXiv:1412.0195 [math.LO], Dec. 2014, 21 p.
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Counterexamples to countable-section Π12 uniformization and Π13 separation, arXiv:1410.2537 [math.LO], Oct. 2014, 18 p.
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A definable $E_0$-class containing no definable elements, arXiv:1408.6642 [math.LO], Aug 2014, 12 p.
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A countable definable set of reals containing no definable elements, arXiv:1408.3901 [math.LO], Aug. 2014, 11 p.
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Linearization of partial quasi-orderings in the Solovay model revisited, arXiv:1408.1202 [math.LO], Aug. 2014, 13 p.
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Bounding and decomposing thin analytic partial orderings, arXiv:1407.0929v2 [math.LO], Jul 2014, 12 p.
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A generalization of Solovay"s Sigma-construction. arXiv:1402.0961 [math.LO]. 5 Feb 2014, 6 p.
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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
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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.
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On countable cofinality of definable chains in Borel partial orders. arXiv:1312.2064 [math.LO]. Sat, 7 Dec 2013
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Surreal numbers from the point of view of nonstandard analysis, Sy David Friedman"s 60th-Birthday Conference, Vienna, Austria, July 2013.
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Felix Hausdorff. Gesammelte Werke, Band IA: Allgemeine Mengenlehre. Berlin: Springer, 2013, xxvi+538 pp., Monograph ISBN: 978-3-642-25598-4.
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Is mathematical history written by the victors? Notices of the AMS, 2013, 60, no 7, pp. 886-904.
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Canonical Ramsey Theory on Polish Spaces. Cambridge University Press, Cambridge, UK, 2013, viii+269 pp., Monograph ISBN 978-1-107-02685-8
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Contemporary Set Theory: absolutely undecidable classical problems. (Russian.) Monograph, published by Independent Moscow university, 2013, 384 pages.
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Kommentar zu [H 1936b], Summen von $aleph_1$ Mengen. In: Felix Hausdorff, Gesammelte Werke. Band Ia: Allgemeine Mengenlehre, Berlin: Springer, 2013, pp. 364-366.
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Kommentar zu [H 1909a], Die Graduierung nach dem Endverlauf. In: Felix Hausdorff, Gesammelte Werke. Band Ia: Allgemeine Mengenlehre, Berlin: Springer, 2013, pp. 336-346.
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Gaps in partially ordered sets and related problems, In: Felix Hausdorff, Gesammelte Werke. Band Ia: Allgemeine Mengenlehre, Berlin: Springer, 2013, pp. 367-405.
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On effective $sigma$-boundedness and $sigma$-compactness, Mathematical Logic Quarterly, 2013, 59, no 3, pp. 147-166.
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Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics, Foundations of Science, 2013, 18, 2, pp. 259-296.
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“Effective Compactness and Sigma-Compactness” Mathematical notes, 2012, Vol. 91, Iss. 6, P. 789–799.
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An infinity which depends on the axiom of choice, Applied Mathematics and Computation, Vol. 218, Iss. 16, April 15 2012, P. 8196–8202,
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On effective compactness and sigma-compactness. arXiv:1103.1060 [math.LO]. Sat, 5 Mar 2011
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On effective sigma-boundedness and sigma-compactness. arXiv:1110.0919 [math.LO]. Wed, 5 Oct 2011.
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An infinity which needs the axiom of choice, Logic Colloquium 2011, Barcelona, 2011, Contributed Talks.
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On effective compactness and sigma-compactness, Third European Set Theory Conference, 3 - 8 July 2011, ICMS, Edinburgh, UK.
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“An effective minimal encoding of uncountable sets” Siberian mathematical journal, 2011, Vol. 52, No. 5, pp. 854–863.
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