## Graduate Student Seminars-Optimal descriptions of computable groups

Title:  Optimal descriptions of computable groups

Speaker: Iva Bilanovic

Date and Time: Friday, December 1, 3:00-4:00pm

Place: Rome 206

Abstract: We will introduce the infinite dihedral group, D, a finitely generated group whose primitive and imprimitive sets of words are both computable given a computable copy of the group. By the Scott Isomorphism Theorem we can describe D by a sentence, in countable infinitary language, whose computable models are exactly the isomorphic copies of the group. The set of Gödel codes for these computable isomorphic copies of D allows us to check that our description is as simple as possible.