LOGIC SEMINAR  Wednesday November 19, 4:00,  412 SEO <br>
SPEAKER: Andre Nies (University of Chicago)<br>
TITLE: Spectra of $\omega_1$-categorical theories<br>
ABSTRACT: If $T$ is an $\omega_1$ categorical but not $\omega$-categorical
theory, then the countable models of $T$ form an elementary chain <br>

$$\A_0 \prec \A_1 \prec \ \ldots \ \prec \A_\omega.$$<br>

Let $SRM(T)$ be the set of those $i \le \omega$ such that $\A_i$ has a
recursive presentation (SRM stands for ``spectrum of recursive 
models'').
 While it can be shown that $SRM(T)$ is
recursive in $\emptyset^{(\omega+4)}$, it is not known which sets can occur as
sets $SRM(T)$. Extending results by  Khoussainov, Nies and Shore we  obtain
examples of theories $T$ such that $SRM(T) = [1, \nu)$, for any $\nu$
such that $1 < \nu \le \omega$. These seem to be the most complicated
spectra obtained so far.