35 citations · 455 across the 85 of their papers we have counts for
8 papers · 1 filter
Cauchy, infinitesimals and ghosts of departed quantifiers
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for t…
Definable minimal collapse functions at arbitrary projective levels
Vladimir Kanovei, Vassily Lyubetsky
Using a non-Laver modification of Uri Abraham's minimal collapse function, we define a generic extension by a real , in which, for a given , $\{a\}…
Minimal axiomatic frameworks for definable hyperreals with transfer
Frederik S. Herzberg, Vladimir Kanovei, Mikhail G. Katz +1
We modify the definable ultrapower construction of Kanovei and Shelah (2004) to develop a ZF-definable extension of the continuum with transfer provable using countable choice only…
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Tiziana Bascelli, Piotr Blaszczyk, Alexandre Borovik +7
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and…
Definable classes at arbitrary projective levels
Vladimir Kanovei, Vassily Lyubetsky
Using a modification of the invariant Jensen forcing, we define a model of ZFC, in which, for a given , there exists a lightface set of reals, which is a ${\mat…
A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory
Vladimir Kanovei, Mikhail G. Katz
Can a positive function on R have zero Lebesgue integral? It depends on how much choice one has. Keywords: Lebesgue integral; Zermelo--Fraenkel theory; Feferman-Levy model