## Journal of Symbolic Logic

### On the $T$-Degrees of Partial Functions

Paolo Casalegno

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741896

Mathematical Reviews number (MathSciNet)
MR805668

Zentralblatt MATH identifier
0585.03014

JSTOR
Casalegno, Paolo. On the $T$-Degrees of Partial Functions. J. Symbolic Logic 50 (1985), no. 3, 580--588. https://projecteuclid.org/euclid.jsl/1183741896