Regularity in models of arithmetic-Reference-Cited by-同舟云学术

Regularity in models of arithmetic

Published:1984-03 Issue:1 Volume:49 Page:272-280
ISSN:0022-4812
Container-title:Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Mills George,Paris Jeff

Abstract

AbstractThis 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference8 articles.

1. ∑n-Collection Schemas in Arithmetic

2. A Mathematical Incompleteness in Peano Arithmetic

3. Mills G. , Extensions of models of Peano arithmetic, Ph.D. dissertation, University of California, Berkeley, California, 1977.

4. Kirby L. , Initial segments of models of arithmetic, Ph.D. dissertation, University of Manchester, Manchester, 1977.

5. Bennett J. , On spectra, Ph.D. dissertation, Princeton University, Princeton, N.J., 1962.

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