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An incompleteness theorem for βn-models

  • Carl Mummert (a1) and Stephen G. Simpson (a2)


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.



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An incompleteness theorem for βn-models

  • Carl Mummert (a1) and Stephen G. Simpson (a2)


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