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.

Time and Place

Tea at 3:30pm in the KGRC meeting room

Talk at 4:00pm in the KGRC lecture room

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.