University Seminar: Logic Across Disciplines- Relatively C-categorical structures

Abstract:  For a computability-theoretic complexity class C, we say that a computable structure A is relatively C-categorical if for every isomorphic structure B, there is an isomorphism that is of complexity C using the atomic diagram of B as an oracle. This notion is more general than C-categoricity and can be expressed syntactically using nice Scott families of formulas. We will give examples from familiar classes of structures and survey recent related results.