THE DEGREE OF DECIDABLE CATEGORICITY OF A MODEL WITH INFINITE SOLUTIONS FOR COMPLETE FORMULAS

We construct a decidable prime model in which the degree of a set of complete formulas is equal to 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 m...

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Bibliographic Details
Published in:Algebra and Logic 2021, Vol.60 (3)
Main Authors: Goncharov, S.S, Marchuk, M.I
Format: Report
Language:English
Subjects:
Algorithms
Mathematical research
Online Access:Get full text
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Summary:We construct a decidable prime model in which the degree of a set of complete formulas is equal to 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.
ISSN:0002-5232
DOI:10.1007/s10469-021-09642-y