Regularity in models of arithmetic

Journal of Symbolic Logic 49 (1):272-280 (1984)
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Abstract

This paper investigates the quantifier "there exist unboundedly many" in the context of first-order arithmetic. An alternative axiomatization is found for Peano arithmetic based on an axiom schema of regularity: The union of boundedly many bounded sets is bounded. We also obtain combinatorial equivalents of certain second-order theories associated with cuts in nonstandard models of arithmetic

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Jeffrey Paris
University of Manchester

Citations of this work

The Stability Spectrum for Classes of Atomic Models.John T. Baldwin & Saharon Shelah - 2012 - Journal of Mathematical Logic 12 (1):1250001-.
Model Theory of the Regularity and Reflection Schemes.Ali Enayat & Shahram Mohsenipour - 2008 - Archive for Mathematical Logic 47 (5):447-464.

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