Kurt Gödel Research Center

2017 seminar talk: News on mad families

Talk held by David Schrittesser (University of Copenhagen, Denmark) at the KGRC seminar on 2017-06-22.

Abstract

This talk is about two results on mad families (dating from this year): Firstly, in joint work with Karen Bakke Haga and Asger Törnquist, we link madness of certain definable sets to forcing and use this to show that under the Axiom of Projective Determinacy there are no projective mad families. Moreover, the results generalize: we may replace "being almost disjoint" by "being J-disjoint", for certain ideals J on the natural numbers including, e.g., Fin x Fin. The other result is an improvement of Horowitz and Shelah's construction of a Borel maximal eventually different family of functions. We obtain a closed such family, and the result even generalizes to certain compact spaces.