Regularity in models of arithmetic

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

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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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