2009 seminar talk: Computable categoricity vs. relative computable categoricity
Talk held by Ekaterina Fokina (KGRC) at the KGRC seminar on 2009-11-12.
The notion of computable categoricity of structures is one of the fundamental in computable model theory. A computable structure A is computably categorical if for every computable structure B isomorphic to A, there exists a computable isomorphism from A to B. We will study the question of syntactical characterization of the notion of computable categoricity. The answer exists only under some additional effectiveness condition. Examination of this characterization without the effectiveness condition will lead us to the notion of relative computable categoricity.