October 2
Java Villano,
University of Toronto
Switching categoricity behavior with a given degree
Given a noncomputable c.e. set D, we can construct a computable structure $G$ such that any two computable copies of $G$ are computably isomorphic while there are two $D$-computable copies of $G$ that are not $D$-computably isomorphic. In other words, $G$ is computably categorical, but not computably categorical relative to $D$. Conversely, we construct a computable structure that is not computably categorical, but is computably categorical relative to $D$. These results differ from those in the literature regarding computable categoricity and its relativizations because the degree $D$ is given instead of constructed. In this talk, we discuss these results and some aspects of the construction regarding the former result.