## Journal of Symbolic Logic

### Degree spectra of prime models

Barbara F. Csima

#### Abstract

We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. We combine the construction used in the proof with other constructions to show that complete decidable atomic theories have low prime models with added properties.

If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 < d0’, there is a prime model with elementary diagram of degree d. Indeed, this is a corollary of the fact that if T is a complete decidable theory and L is a computable set of c.e. partial types of T, then for any Δ02 degree d > 0, T has a d-decidable model omitting the nonprincipal types listed by L.

#### Article information

Source
J. Symbolic Logic, Volume 69, Issue 2 (2004), 430-442.

Dates
First available in Project Euclid: 19 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1082418536

Digital Object Identifier
doi:10.2178/jsl/1082418536

Mathematical Reviews number (MathSciNet)
MR2058182

Zentralblatt MATH identifier
1069.03025

#### Citation

Csima, Barbara F. Degree spectra of prime models. J. Symbolic Logic 69 (2004), no. 2, 430--442. doi:10.2178/jsl/1082418536. https://projecteuclid.org/euclid.jsl/1082418536

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