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...
In [2] a construction of a class of two-intersection sets with respect to hyperplanes in PG(r - 1, qt ), rt even, is given, with the same parameters as the union of (qt/2 - 1)/(q ...
Abstract. We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient ...
Assume that there is no quasi-measurable cardinal not greater than 2ω . We show that for a c.c.c. σ-ideal I with a Borel base of subsets of an uncountable Polish space, if A is a...
We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest su...