Journal of Symbolic Logic

Regularity in Models of Arithmetic

George Mills and Jeff Paris

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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.

Article information

Source
J. Symbolic Logic, Volume 49, Issue 1 (1984), 272-280.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741493

Mathematical Reviews number (MathSciNet)
MR736621

Zentralblatt MATH identifier
0584.03044

JSTOR
links.jstor.org

Citation

Mills, George; Paris, Jeff. Regularity in Models of Arithmetic. J. Symbolic Logic 49 (1984), no. 1, 272--280. https://projecteuclid.org/euclid.jsl/1183741493


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