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Regularity in models of arithmetic

Published online by Cambridge University Press:  12 March 2014

George Mills  and
Jeff Paris
George Mills
Affiliation:
Carleton College, Northfield, Minnesota 55057
Jeff Paris
Affiliation:
University of Manchester, Manchester ML3 9PL, England
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 1 , March 1984 , pp. 272 - 280
Copyright
Copyright © Association for Symbolic Logic 1984

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References

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