Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 49, Issue 1 (1984), 272-280.
Regularity in Models of Arithmetic
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.
J. Symbolic Logic, Volume 49, Issue 1 (1984), 272-280.
First available in Project Euclid: 6 July 2007
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Mills, George; Paris, Jeff. Regularity in Models of Arithmetic. J. Symbolic Logic 49 (1984), no. 1, 272--280. https://projecteuclid.org/euclid.jsl/1183741493