Definable selector for $\Delta^0_2$ 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 by Journal Citation Reports JCR and SCImago SJR.)
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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
SCOPUS, Q2 Go to publication

Definable elements of definable Borel sets.
Mathematical Notes,
2019, 105, no 5, pp. 684-693.
DOI: 10.1134/S0001434619050055
SCIMAGO, Q2
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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
SCIMAGO Q1 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
WoS Q1
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On Harrington"s model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami.
arXiv:1810.12542 [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
WoS Q3 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
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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
WoS Q2 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:1712.00769 [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
[SCIMAGO, Q2] 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
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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

A countable definable set containing no definable elements.
Mathematical Notes, Sep 2017, Vol. 102, Iss. 3–4, P. 338–349.
doi:10.1134/S0001434617090048
[SCIMAGO, Q2] Go to publication

2017 year

Authors: Blazczyk P., Kanovei V., Katz M., Sherry D.

Controversies on foundations of analysis: comments on Schubring’s conflicts.
Foundations of Science, 2017, 22, 1, pp. 125--140.
DOI:
10.1007/s10699-015-9473-4 .
WoS Q2 Go to publication

A Groszek-Laver pair of undistinguishable E_{0}-classes.
Mathematical Logic Quarterly, 2017, Vol. 63, No. 1–2, P. 19–31.
doi:10.1002/malq.201500020
WoS Q3 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

2016 year

Authors: Błaszczyk P., Borovik A., Kanovei V., Katz M., et al.

A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos.
Logica Universalis,
2016, 10, pp. 393-405.
DOI
10.1007/s11787-016-0153-0
SCOPUS Q3 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.
DOI:
10.1007/s40509-016-0074-x 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.
DOI: 10.1016/j.apal.2015.12.002
WoS Q1 Go to publication