John Baldwin : Intertwining Model theory and set theory

Posted by , part of the Logic Seminar.

At

Nov. 22, 2011, 4 p.m.

In

SEO 427

Abstract

We describe techniques (ultralimits and omitting types theorem) for constructing models of set theory with prescribed properties. Then we use these properties of models of set theory to prove in ZFC theorems about $L_{\omega_1,\omega}$ and $PC\Gamma(\aleph_0,\aleph_0)$ classes. E.g. absoluteness of existence of a model in $\aleph_1$ (this proof by Larson), few models in $\aleph_1$ implies small (in any fragment of $L_{\omega_1,\omega}(aa))$ (Larson (earlier Keisler)) and for aec (Baldwin/Larson), almost Galois $\omega$-stability and few models in $\aleph_1$ implies Galois $\omega$-stability (Baldwin/Larson/Shelah).

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