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June 2004 An incompleteness theorem for βn-models
Carl Mummert, Stephen G. Simpson
J. Symbolic Logic 69(2): 612-616 (June 2004). DOI: 10.2178/jsl/1082418545

Abstract

Let n be a positive integer. By a βn-model we mean an ω-model which is elementary with respect to Σ1n 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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Carl Mummert. Stephen G. Simpson. "An incompleteness theorem for βn-models." J. Symbolic Logic 69 (2) 612 - 616, June 2004. https://doi.org/10.2178/jsl/1082418545

Information

Published: June 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1075.03031
MathSciNet: MR2058191
Digital Object Identifier: 10.2178/jsl/1082418545

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 2 • June 2004
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