Title: Large Infinite Combinatorics and Definability
Author: Arnold W. Miller
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 infinite subsets of {0,1,2,..} 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 omega_2 cover of reals by
Borel sets has an omega_1 subcover. We show that if
V=L then there are Pi^1_1 Hamel bases, maximal almost disjoint families,
and maximal independent families.