Matthew Harrison-Trainor, Pure Mathematics University of Waterloo
“Pairs of computable structures”
Let A and B be two structures over the same language. We consider the question of which sets S can be coded by those structures as follows: there is a uniformly computable sequence of structures (Cn)n ∈ ω such that Cn is isomorphic to A if n ∈ S and to B otherwise. We will give some examples, and then show that Πn sets can be coded by structures which are n-friendly and satisfy the nth back-and-forth relation.