Coanalytic families of functions

Abstract

For Van Douwen families, maximal families of eventually different permutations and maximal ideal independent families we show that the existence of a ${\Sigma }_2^1$ family implies the existence of a ${\Pi }_1^1$ family of the same size. We also prove a similar, but slightly weaker result for generating sets of cofinitary groups.

arXiv comment12 pages; submitted