148 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Institute for Information Transmission ProblemsRU14 papers
- Bar-Ilan UniversityIL10 papers
- Institute of Professional InnovationsRU6 papers
- Northern Arizona UniversityUS6 papers
- Uniwersytet Komisji Edukacji Narodowej w KrakowiePL6 papers
- Lomonosov Moscow State UniversityRU4 papers
- North Dakota State UniversityUS4 papers
- Novosibirsk State UniversityRU3 papers
- Russian Academy of SciencesRU3 papers
- Russian RailwaysRU3 papers
- Sobolev Institute of MathematicsRU3 papers
- Bauman Moscow State Technical UniversityRU2 papers
10 papers · 1 filter
Gregory's sixth operation
Tiziana Bascelli, Piotr Blaszczyk, Vladimir Kanovei +6
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under sc…
A generic property of Solovay's set
Vladimir Kanovei, Vassily Lyubetsky
We prove that Solovay's set is generic over the ground model via a forcing notion whose order relation -extends the given order relation.
Toward a history of mathematics focused on procedures
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +3
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Thei…
Countable OD sets of reals belong to the ground model
Vladimir Kanovei, Vassily Lyubetsky
It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension that every countable ordinal-definable set of reals belongs to to the ground universe
In Cohen generic extension, every countable OD set of reals belongs to the ground model
Vladimir Kanovei
It is true in the Cohen generic extension of L, the constructible universe, that every countable ordinal-definable set of reals belongs to L.
Is Leibnizian calculus embeddable in first order logic?
Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz +4
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus o…
Interpreting the infinitesimal mathematics of Leibniz and Euler
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
We apply Benacerraf's distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations…
Small oscillations of the pendulum, Euler's method, and adequality
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1
Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well…
OD elements of countable OD sets in the Solovay model
Vladimir Kanovei
It is true in the Solovay model that every countable ordinal-definable set of sets of reals contains only ordinal-definable elements.
Controversies in the foundations of analysis: Comments on Schubring's Conflicts
Piotr Blaszczyk, Vladimir Kanovei, Mikhail Katz +1
Foundations of Science recently published a rebuttal to a portion of our essay it published two years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his…