In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2ω is a Gδσ-set then either...
The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver ([19]) and Harrington-K...
Ekaterina B. Fokina, Sy-David Friedman, Asger T&ou...
This paper is a continuation of the study of topological properties of omega context free languages (-CFL). We proved in [Topological Properties of Omega Context Free Languages, T...
We prove that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the i...
In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to "Every set has the s...