Logic Seminar
John Baldwin
UIC
Uncountable models still count
Abstract: I will discuss approaches to Vaught's Conjecture by counting the number of models with cardinality $
\aleph_1$. The main actual result will be a theorem of Gao: An infinite structure $M$ is totally
categorical if and only if the automorphism group of $M$ admits a complete left-invariant metric. We will
observe that that fact prevents naive attempts to construct sentences of $\mathcal L_{\omega_1,\omega}$
with a prescribed number of models of cardinality $\aleph_1$.
Tuesday February 14, 2006 at 4:00 PM in SEO 427