A. H. Lachlan, Robert Irving Soare
Abstract
Abstract 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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Abstract 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.
Key concepts: Arithmetic, Arithmetic circuit complexity, Mathematics, Arbitrary-precision arithmetic, Saturation arithmetic, Affine arithmetic, Forcing (mathematics), Second-order arithmetic