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Transactions of the American Mathematical Society

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

 

 

Prime and search computability, characterized as definability in certain sublanguages of constructible $ L\sb{\omega }{}\sb{1,\omega }$


Author: Carl E. Gordon
Journal: Trans. Amer. Math. Soc. 197 (1974), 391-407
MSC: Primary 02F27; Secondary 02B25
DOI: https://doi.org/10.1090/S0002-9947-1974-0416882-2
MathSciNet review: 0416882
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Abstract: The prime computable (respectively, search computable) relations of an arbitrary mathematical structure are shown to be those relations R such that both R and its complement are definable by disjunctions of recursively enumerable sets of quantifier free (respectively, existential) formulas of the first order language for the structure. The prime and search computable functions are also characterized in terms of recursive sequences of terms and formulas of this language.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0416882-2
Keywords: Primitive computable, prime computable, search computable, infinitary language
Article copyright: © Copyright 1974 American Mathematical Society