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Explore the concept of relativized computable categoricity in this 43-minute conference talk from the Workshop on "Reverse Mathematics: New Paradigms" at the Erwin Schrödinger International Institute for Mathematics and Physics. Learn how computable categoricity can be relativized to specific Turing degrees, where a computable structure A is computably categorical relative to degree d if all d-computable copies have d-computable isomorphisms to A. Discover the notable behaviors of this notion within Turing degrees, including its nonmonotonic properties below 0', and examine which classes of structures can provide computable witnesses to these behaviors. The presentation draws from recent research findings published in mathematical preprints, offering insights into the intersection of computability theory and reverse mathematics.
