Models of arithmetic and upper Bounds for arithmetic sets

Journal of Symbolic Logic 59 (3):977-983 (1994)
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We settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions



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Computability in structures representing a Scott set.Alex M. McAllister - 2001 - Archive for Mathematical Logic 40 (3):147-165.

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Upper bounds for the arithmetical degrees.M. Lerman - 1985 - Annals of Pure and Applied Logic 29 (3):225-254.

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