Logic Seminar
Dave Sahota
UIC
Countable Models of an O-minimal Theory
Abstract: Mayer showed a strong form of Vaught's Conjecture for o-minimal theories: if $T$ has fewer than $2^\omega$ countable models, then $T$ has $6^a3^b$ countable models for some natural numbers $a$ and $b$. We will show if $T$ has $2^\omega$ countable models, then if all $p(x)\in S_1(A)$ for any finite set $A$ are simple, then the class of countable models of T is Borel Reducible to the class of countable subsets of $2^\omega\times6$ by $M\mapsto\{(p,i)$ : the realizations of $p$ in $M$ are of form $i\}$; if any $p(x)\in S_1(A)$ is non-simple for some finite set $A$, then there is a finite set $B$ such that the class of countable models of $T$ over $B$ is Borel Complete.
Tuesday April 10, 2012 at 4:00 PM in SEO 427