An unpublished theorem of Solovay, revisited.
Journal of Mathematical Logic, 2020. Online first.
DOI: 10.1142/S0219061321500148
WoS Q1. Go to publication

Models of set theory in which separation theorem fails.
Izvestiya: Mathematics, 2021, Vol. 85, No 6,
to appear.
DOI: 10.1070/IM8937
WoS Q2 Go to publicationDownload (231 KB)

Factoring Solovay-random extensions, with application to the Reduction property.
Monatshefte fur Mathematik, 2020.
Online first.
DOI: 10.1007/s00605-020-01482-9
WoS Q2. Go to publication

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
(WoS Q1) Go to publication

Metric completions, Heine-Borel, and approachability.
Open Mathematics, 2020, Volume 18, Issue 1, 162-166.
DOI: 10.1515/math-2020-0017
WoS Q3 Go to publication

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 E_{0}-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
Go to publication

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
Go to publication

Definable selector for Δ^{0}_{2} 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
(WoS Q2) Go to publication

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 E_{0} 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) Go to publication

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
WoS Q2 Go to publication

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
WoS Q2 Go to publication

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)
Go to publication

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) Go to publication

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
SCIMAGO, Q3 Go to publication

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 Go to publication

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 .
WoS Q2
Go to publication

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 .
WoS Q2
Go to publication

2017 year

Authors: Bair J., Blaszczyk P., Ely R., Henry V., Kanovei V., Katz K., Katz M., et al.

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 Go to publication