5 papers
Locally countable graphs of second projective class not generated by countably many projective functions
Vladimir Kanovei, Vassily Lyubetsky
To answer a question by Rettich and Serafin, we define a model of set theory in which there exists a locally countable graph on a subset of the real line, which is not…
A philosophical history of infinitesimals
Vladimir Kanovei, Mikhail G. Katz, Taras Kudryk +1
We explore the issue of providing a foundational framework for Leibnizian infinitesimals in the light of modern standard and nonstandard approaches. We outline a trichotomy of ordi…
On Petr Novikov's problem of ordered systems of uniform sets
Vladimir Kanovei, Vassily Lyubetsky
We prove that every ordinal is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result give…
On the significance of parameters and the projective level in the Choice and Comprehension axioms
Vladimir Kanovei, Vassily Lyubetsky
We make use of generalized iterations of Jensen forcing to define a cardinal-preserving generic model of ZF for any and each of the following four Choice hypotheses: (1) $…
Notes on the equiconsistency of ZFC without the Power Set axiom and second order PA
Vladimir Kanovei, Vassily Lyubetsky
We demonstrate that theories , , (minus means the absence of the Power Set axiom) and , (minus means the absenc…