Logic Seminar
John Baldwin
UIC
Intertwining Model theory and set theory
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).
There will be tea in SEO300 at 3:30p
Tuesday November 22, 2011 at 4:00 PM in SEO 427