Jesse Johnson : Computable categoricity and quasiminimal-excellent classes.

Posted by Isaac Goldbring , part of the Logic Seminar.

At

April 25, 2013, 3 p.m.

In

SEO 427

Abstract

We will introduce some basic notions of $\alpha$-recursion as applied to computable structure theory. We will give a few easy examples of ``computable" structures and "computably categorical" structures. Using these notions, we will give a computability-theoretic analysis of quasiminimal-excellent classes. We show that for any quasiminimal-excellent class (with infinite-dimensional models) and any successor $\kappa^+ \geq \aleph_1$, the member of dimension $\kappa^+$ has a computable copy and is relatively $\Delta^0_2$-categorical. We then give precise conditions under which the member of size $\kappa^+$ is relatively-computably categorical.