Infinite combinatorics and definability

Abstract

AbstractThe topic of this paper is Borel versions of infinite combinatorial theorems. For example it is shown that there cannot be a Borel subset of [ω]ω which is a maximal independent family. A Borel version of the delta systems lemma is proved. We prove a parameterized version of the Galvin-Prikry Theorem. We show that it is consistent that any ω2 cover of reals by Borel sets has an ω1 subcover. We show that if V \= L, then there are π11 Hamel bases, maximal almost disjoint families, and maximal independent families