On the t-degrees of partial functions

Journal of Symbolic Logic 50 (3):580-588 (1985)
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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DOI 10.2307/2274313
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