Kurt Gödel Research Center

2018 seminar talk: The Ramsey property, MAD families, and their multidimensional relatives

Talk held by David Schrittesser (KGRC) at the KGRC seminar on 2018-10-25.

Abstract

Suppose every set of real numbers has the Ramsey property and “uniformization on Ellentuck-comeager sets” as well as Dependent Choice hold (as is the case under the Axiom of Determinacy, but also in Solovay's model). Then there are no MAD families. As it turns out, there are also no (Fin x Fin)-MAD families, where Fin x Fin is the two-dimensional Fubini product of the ideal of finite sets. We also comment on higher dimensional products.

All results are joint work with Asger Törnquist.

Slides are available here, a video recording of this talk is available on YouTube.