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Regularity in models of arithmetic
Journal of Symbolic Logic 49 (1):272-280 (1984)
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 arithmeticAuthor's Profile
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Citations of this work
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Model theory of the regularity and reflection schemes.Ali Enayat & Shahram Mohsenipour - 2008 - Archive for Mathematical Logic 47 (5):447-464.
Weak forms of the Regularity Principle in the presence of equation image.Charalampos Cornaros - 2013 - Mathematical Logic Quarterly 59 (1-2):84-100.
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