This article is cited in 1 paper

The degree of decidable categoricity of a model with infinite solutions for complete formulas

S. S. Goncharov^ab, M. I. Marchuk<sup>a

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: We construct a decidable prime model in which the degree of a set of complete formulas is equal to $\mathbf{0}'$, infinitely many tuples of elements comply with every complete formula, and the decidable categoricity spectrum coincides with the set of all $PA$-degrees.

Keywords: computable model, decidable model, computable categoricity, autostability relative to strong constructivizations, degree of decidable categoricity, decidable categoricity spectrum, $PA$-degree.

UDC: 510.5+512.563

Received: 15.07.2021
Revised: 18.10.2021

 English version: Algebra and Logic, 2021, 60:3, 200–206

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