Toronto Set Theory

Event Information The Ramsey property, MAD families, and their multidimensional relatives
13:30 on Friday February 15, 2019
15:00 on Friday February 15, 2019
FI210, Fields Institute, 222 College St.
David Schrittesser

Kurt Gödel Research Center

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.

Results are joint work with Asger Törnquist.