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Seminars "Proof Theory" and "Logic Online Seminar"
April 11, 2023 18:30, Moscow, Zoom


The degrees of relative computable categoricity

I. Sh. Kalimullin

Kazan (Volga Region) Federal University



Abstract: For a Turing degree $\mathbf x$ a computable algebraic structure $\mathcal A$ is relatively $\mathbf x$-computable categorical if there is an $\mathbf x$-computable family of existential formulas defining the automorphism orbits of tuples from $\mathcal A$. We will study the collection of Turing degrees $\mathbf x$ for which a particular computable structure is relatively $\mathbf x$-computable categorical. This consideration also will give a series of unexpected results in the classical recursion theory context.

Language: English


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