Models of set theory in which nonconstructible reals first appear at a given projective level .
Mathematics, 2020, Volume 8, Number 6, Article No 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 J. Form. Logic, 2020, Volume 61, Number 1, 117-128.
DOI: 10.1215/00294527-2019-0034
SCIMAGO, Q2. Go to publication

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.

On mathematical realism and applicability of hyperreals.
Antiquitates Mathematicae, 2019, 13, 1, pp. 19-49.
DOI:10.14708/am.v13i1.6440
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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
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Absoluteness of the Solovay set Σ.
Siberian Mathematical Journal,
2019, 60, no 6, pp. 1003-1006.
DOI: 10.1134/S0037446619060089
SCIMAGO, Q2
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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
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Definable elements of definable Borel sets.
Mathematical Notes,
2019, 105, no 5, pp. 684-693.
DOI: 10.1134/S0001434619050055
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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
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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
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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.
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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
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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
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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
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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
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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 .
WoS Q2
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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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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 .
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A countable definable set containing no definable elements.
Mathematical Notes, Sep 2017, Vol. 102, Iss. 3–4, P. 338–349.
doi:10.1134/S0001434617090048
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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 .
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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
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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. Go to publication