Type: Article

Cofinalities of Borel ideals

Michael Hrušák, Diego Rojas Rebolledo, Jindrich Zapletal;

Abstract:

We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented F sigma ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant b and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.