Martin Zeman : Self-generic structures for ideals on $\omega_2$

Posted by Isaac Goldbring , part of the Logic Seminar.

At

Nov. 5, 2013, 4 p.m.

In

SEO 427

Abstract

The talk focuses on ideals on $\omega_2$ and associated generic embeddings. Such generic embeddings arise in set theory naturally, and their existence has important impact on combinatorics at small cardinals and on the structure of sets of reals. For this reason, some set theorists view them as possible alternatives for large cardinal axioms. One of the most well-known open problem concerning ideals on $\omega_2$ is the saturation of the non-stationary ideal on $\omega_2$ restricted to cof$(\omega_1)$. We formulate a weakening of this property in terms of self-generic structures which is interesting on its own, prove it is consistent relative to large cardinals, and show it has large cardinal strength. This is a joint work with Sean Cox.