Journal of Symbolic Logic

On the $T$-Degrees of Partial Functions

Paolo Casalegno

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Let $\langle\mathscr{T},\leq\rangle$ be the usual structure of the degrees of unsolvability and $\langle\mathscr{D},\leq\rangle$ the structure of the $T$-degrees of partial functions defined in [7]. We prove that every countable distributive lattice with a least element can be isomorphically embedded as an initial segment of $\langle\mathscr{D},\leq\rangle$: as a corollary, the first order theory of $\langle\mathscr{D},\leq\rangle$ is recursively isomorphic to that of $\langle\mathscr{T},\leq\rangle$. We also show that $\langle\mathscr{D},\leq\rangle$ and $\langle\mathscr{T},\leq\rangle$ are not elementarily equivalent.

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J. Symbolic Logic, Volume 50, Issue 3 (1985), 580-588.

First available in Project Euclid: 6 July 2007

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Casalegno, Paolo. On the $T$-Degrees of Partial Functions. J. Symbolic Logic 50 (1985), no. 3, 580--588.

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