Fri Sep 7, 2012
60 Evans Hall, 4–6 PM
Maraynthe Malliaris (University of Chicago)
Saturation of Ultrapowers and the Structure of Unstable Theories
Abstract: The talk will be about some very recent progress on Keisler’s order, a far-reaching program of understanding basic model-theoretic structure through the lens of regular ultrapowers. The focus of the talk will be on classification of unstable theories; some applications to problems in set theory/general topology will also be mentioned, including a recent result of Malliaris and Shelah solving the oldest problem on cardinal invariants of the continuum.
I will assume basic familiarity with ultraproducts, Łoś´s theorem, and saturation, and plan to give most other relevant definitions. Papers mentioned in the talk are available at http://math.uchicago.edu/~mem.