20 citations · 140 across the 30 of their papers we have counts for
32 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…
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 gives…
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…
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) $…
The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic
Vladimir Kanovei, Vassily Lyubetsky
The parameter-free part of , the 2nd order Peano arithmetic, is considered. We make use of a product/iterated Sacks forcing to define an -model o…
A model in which the Separation principle holds for a given effective projective Sigma-class
Vladimir Kanovei, Vassily Lyubetsky
In this paper, we prove the following: If , there is a generic extension of -- the constructible universe -- in which it is true that the Separation principle holds for…