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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Type structure complexity and decidability


Author: T. S. Millar
Journal: Trans. Amer. Math. Soc. 271 (1982), 73-81
MSC: Primary 03C15; Secondary 03B25, 03D35
DOI: https://doi.org/10.1090/S0002-9947-1982-0648078-8
MathSciNet review: 648078
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Abstract: We prove that for every countable homogeneous model $ \mathcal{A}$ such that the set of recursive types of $ \operatorname{Th} (\mathcal{A})$ is $ \sum _2^0$, $ \mathcal{A}$ is decidable iff the set of types realized in $ \mathcal{A}$ is a $ \sum _2^0$ set of recursive types. As a corollary to a lemma, we show that if a complete theory $ T$ has a recursively saturated model that is decidable in the degree of $ T$, then $ T$ has a prime model.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0648078-8
Article copyright: © Copyright 1982 American Mathematical Society

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