Definable minimal collapse functions at arbitrary projective levels. Journal of symbolic logic. Submitted

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. DOI: https://doi.org/10.1070/IM8521
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Definable minimal collapse functions at arbitrary projective levels. July 2017, arXiv:1707.07320 [math.LO], pp. 1-30.
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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.
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Cauchy"s infinitesimals, his sum theorem, and foundational paradigms. Foundations of Science, 2017, First Online 27 June 2017, DOI: https://doi.org/10.1007/s10699-017-9534-y
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The full basis theorem does not imply analytic wellordering. February 2017, arXiv:1702.03566 [math.LO], pp. 1-63.
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Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 2017, accepted.
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Countable OD sets of reals belong to the ground model, Archive for Mathematical Logic, 2017, First Online 24 June 2017, DOI: https://doi.org/10.1007/s00153-017-0569-0
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A positive function with vanishing Lebesgue integral in ZF. Real Analysis Exchange, 2017, 42, no. 2, to appear.
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Gregory"s sixth operation, Foundations of Science, 2017. First Online 20 December 2016, DOI: https://doi.org/10.1007/s10699-016-9512-9
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Minimal axiomatic frameworks for definable hyperreals with transfer. Journal of Symbolic Logic, 2017, to appear. DOI: 10.1017/jsl.2017.48

Interpreting the infinitesimal mathematics of Leibniz and Euler, Journal of General Philosophy of Science, 2017, 48, issue 2, pp, 195--238. DOI: https://doi.org/10.1007/s10838-016-9334-z
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A definable countable set not containing definable elements, Mathematical notes, 2017, 102, no. 3, pp. 45–56 (in Russian).
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Controversies on foundations of analysis: comments on Schubring’s conflicts. Foundations of Science, 2017, 22, 1, pp. 125--140. DOI: https://doi.org/10.1007/s10699-015-9473-4
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A Groszek-Laver pair of undistinguishable E₀-classes. Mathematical Logic Quarterly, 2017, 63, No. 1–2, pp. 19–31. doi:10.1002/malq.201500020.
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A generic property of Solovay"s set Σ. November 2016, arXiv:1611.00176 [math.LO], pp. 1-4.
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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 https://doi.org/10.1007/s11787-016-0153-0
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Toward a history of mathematics focused on procedures, Foundations Of Science, 2016, First Online 21 September 2016, DOI: https://doi.org/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, 3, no 3, pp 231–236. DOI: https://doi.org/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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Is Leibnizian calculus embeddable in first order logic? Foundations of Science, First Online: 22 June 2016, DOI: https://doi.org/10.1007/s10699-016-9495-6
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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: https://doi.org/10.1016/j.apal.2015.12.002
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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: https://doi.org/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: https://doi.org/10.1016/j.amc.2014.06.037
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Euler"s lute and Edward"s oud. Mathematical Intelligencer, 2015, 37, 4, pp. 48--51. DOI: https://doi.org/10.1007/s00283-015-9565-6
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A definable $E_0$ class containing no definable elements, Archive for Mathematical Logic, 2015, 54, 5, pp. 711--723. DOI: https://doi.org/10.1007/s00153-015-0436-9
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Generalization of one construction by Solovay, Siberian Mathematical Journal, 2015, 56, no. 6, pp. 1072–1079. DOI: https://doi.org/10.1134/S0037446615060117
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Proofs and retributions, Foundations of Science, 2015, 20, 1, pp 1-25. DOI: https://doi.org/10.1007/s10699-013-9340-0
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On effective σ-boundedness and σ-compactness in Solovay"s model, Mathematical notes, 2015, 98, 1-2, pp. 273--282. DOI: https://doi.org/10.1134/S0001434615070299
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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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