An incompleteness theorem for βn-models
Copyright policy )An incompleteness theorem for βn-models
Abstract.Let n be a positive integer. By a βn-model we mean an ω-model which is elementary with respect to formulas. We prove the following βn-model version of Gödel's Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a βn-model of S, then there exists a βn-model of S + “there is no countable βn-model of S”. We also prove a βn-model version of Löb's Theorem. As a corollary, we obtain a βn-model which is not a βn+1-model.
- Pennsylvania State University United States
Models of arithmetic and set theory, model, second-order arithmetic, Gödel, incompleteness, Second- and higher-order arithmetic and fragments, Foundations of classical theories (including reverse mathematics)
Models of arithmetic and set theory, model, second-order arithmetic, Gödel, incompleteness, Second- and higher-order arithmetic and fragments, Foundations of classical theories (including reverse mathematics)
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