Kurt Gödel Research Center

2007 seminar talk: Reflection principles and pcf theory

Talk held by Matteo Viale (KGRC) at the KGRC seminar on 2007-11-15.

Abstract

We present some application of reflection principles to the analysis of the partial order of reduced product of regular cardinal. The guiding example being the study of the partial order (\prod_n\aleph_n,<^*), where f<^*g if for finitely many n f(n)\geq g(n). The main original result is that a reflection principle on \aleph_2 which is equiconsistent with \aleph_2 being weakly compact in L and which follows from Martin's maximum implies that club many points of cofinality \aleph_2 below \aleph_{\omega+1} are approachable. This is obtained by a combination of two theorems: one by me and the other by Assaf Sharon. We also apply this result to deny many instances of Chang conjectures.

The first seminar will be an introduction to the subject. In the second one we will focus on the new results.