Abstract
The 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 ω 2 cover of reals by Borel sets has an ω 1 subcover. We show that if V \\= L, then there are π 1 1 Hamel bases, maximal almost disjoint families, and maximal independent families.
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