Problem Reducibility of a Weakened Version of Ginsburg–Sands Theorem

Explore the problem reducibility of a weakened version of the Ginsburg-Sands theorem in this 50-minute conference lecture from the Workshop on "Reverse Mathematics: New Paradigms" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of computable categoricity and its relativization to specific Turing degrees, examining how a computable structure A is computably categorical if all computable copies B have a computable isomorphism between A and B. Learn about the relativized version where a computable structure A is computably categorical relative to degree d when all d-computable copies B possess a d-computable isomorphism between A and B. Discover the notable behaviors of this notion within Turing degrees, particularly its nonmonotonicity below 0', and investigate which classes of structures can provide computable witnesses to these behaviors. The presentation draws from recent research available at https://arxiv.org/abs/2401.06641 and https://arxiv.org/abs/2505.15706, offering insights into advanced topics in reverse mathematics and computability theory.