Sam Eisenstat, Department of Pure Mathematics, University of Waterloo
“Background for Computable Abelian Group Theory (continued)”
We finish our discussion of definitions in computable model theory, looking at the complexity of presentations of structures and isomorphisms between structures. We also prove a theorem of Mal’cev that we stated last time, which shows that computable structures can be isomorphic without being computably isomorphic.
and, time permitting...
“Properties of Computable Abelian Groups”
Abstract: In this talk, we extend the previously given definitions of computable and c.e. presentations to other members of the arithmetical hierarchy. We also discuss a proof of Smith on computable embeddings of a group into its divisible hull. Time permitting, we remark briefly on computability of torsion abelian groups and begin a discussion of computable and c.e. torsion-free abelian groups.