An unpublished theorem of Solovay, on OD partitions of reals into two non-OD parts, revisited.
Journal of Mathematical Logic, 2021. Online ready 26 December 2020.
DOI: 10.1142/S0219061321500148
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Models of set theory in which separation theorem fails.
Izvestiya: Mathematics, 2021, Vol. 85, No 6,
to appear.
DOI: 10.1070/IM8937
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Factoring Solovay-random extensions, with application to the Reduction property.
Monatshefte fur Mathematik, 2021, 194, 1, pp. 105–117.
DOI: 10.1007/s00605-020-01482-9
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The full basis theorem does not imply analytic wellordering,
Annals of pure and applied logic, 2021, volume 172, issue 4, paper no 102929.
DOI: 10.1016/j.apal.2020.102929
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On the "definability of definable" problem of Alfred Tarski.
Mathematics,
2020, Vol. 8, No. 12, Art. 2214.
DOI: 10.3390/math8122214
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Models of set theory in which nonconstructible reals first appear at a given projective level .
Mathematics,
2020, Vol. 8, No. 6, Art. 910.
DOI: 10.3390/math8060910
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Metric completions, Heine-Borel, and approachability.
Open Mathematics, 2020, Volume 18, Issue 1, 162-166.
DOI: 10.1515/math-2020-0017
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2020 year
Authors: Bair J., Blaszczyk P., Heinig P., Kanovei V., Katz M., McGaffey T.
Cauchy"s work on integral geometry, centers of curvature, and other applications of infinitesimals.
Real Analysis Exchange, 2020,
Vol. 45, No. 1, pp. 127-150 .
DOI: 10.14321/realanalexch.45.1.0127 Go to publication
Canonization of smooth equivalence relations on infinite-dimensional E0-large products.
Notre Dame Journal of Formal Logic,
2020, Vol. 61, No. 1, P. 117–128.
DOI: 10.1215/00294527-2019-0034 Go to publication
Set theory: absolute undecidability of classical problems.
Textbook for universities, 2nd ed., Moscow, Urait, 2019, 348 p. (in Russian).
ISBN: 978-5-534-10390-8
2019 year
Authors: Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., Kutateladze S., Nowik T., Schaps D., Sherry D.
Gregory’s Sixth Operation.
Mircea Pitici (Editor), The Best Writing on Mathematics 2019 Princeton University Press, 2019, pp. 195–207.
DOI: 10.1515/9780691197944-015
Book DOI: 10.1515/9780691197944
Online ISBN: 9780691197944
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2019 year
Authors: Bair J., Blaszczyk P., Kanovei V., Katz M., Heinig P.
19th-century real analysis, forward and backward.
Antiquitates Mathematicae, 2019, 13, 1, pp. 19-49.
DOI:10.14708/am.v13i1.6440
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Definable selector for Δ02 sets modulo countable.
arXiv: 1910.00926 [math.LO],
October 2019 Go to publication
2019 year
Authors: Bottazzi E., Kanovei V., Katz M., Mormann T., Sherry D.
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 Go to publication
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 Go to publication
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
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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 Go to publication
Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v3 [math.LO], January 2018. Go to publication
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. Go to publication
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
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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 Go to publication
2018 year
Authors: Bascelli T., Blazczyk P., Borovik A., Kanovei V., Katz K., Katz M., Kutateladze S., McCaffery T., Schaps D., Sherry D.
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
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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 Go to publication
2018 year
Authors: Bascelli T., Blaszczyk P., Kanovei V., Katz K., Katz M., et al.
Gregory"s sixth operation,
Foundations of Science, 2018, 23, 1, pp. 133--144.
DOI: 10.1007/s10699-016-9512-9
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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
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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
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Minimal axiomatic frameworks for definable hyperreals with transfer.
arXiv:1707.00202 [math.LO], July 2017. Go to publication
2017 year
Authors: Bair J., Blaszczyk P., Ely R., Henry V., Kanovei V., Katz K., Katz M., Kudryk T., Kutateladze S., McGaffey T., Mormann T., Schaps D., Sherry D.
Cauchy, infinitesimals and ghosts of departed quantifiers,
Mat. Stud. 2017, 47, 2, 115--144
doi:10.15330/ms.47.2.115-144 Go to publication
Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy.
arXiv:1712.00769v1 [math.LO], December 2017. Go to publication
A generic property of the Solovay set Σ.
Siberian Mathematical Journal,
2017, Vol. 58, Iss. 6, P. 1012–1014.
doi:10.1134/S0037446617060106 Go to publication
2017 year
Authors: Fletcher P., Hrbacek K., Kanovei V., Katz M., Lobry C., Sanders S.
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
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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
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2017 year
Authors: Blaszczyk P., Kanovei V., Katz M., et al.
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 .
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2017 year
Authors: Blaszczyk Piotr, Kanovei V., U. Katz Karin, G. Katz Mikhail, et al.
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 .
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