**Title:** Computable Classification Problem

**Speaker:** Valentina Harizanov, GWU __http://home.gwu.edu/~harizanv/__**Date and Time:** Thursday, November 2, 2017, 02:30pm-03:30pm

**Place:** Rome Hall 771

**Abstract: ** The Scott Isomorphism Theorem says that for any countable structure *M* there is a sentence, in countable infinitary language, the countable models of which are exactly the isomorphic copies of *M*. Here, we consider a computable structure *A* and define its index set to be the set of all GĂ¶del codes for computable isomorphic copies of *A*. We will present evidence for the following thesis. To calculate the precise complexity of the index set of A, we need a good description of A, using computable infinitary language, and once we have an optimal description, the exact complexity within a computability-theoretic hierarchy will match that of the description.