zbMATH — the first resource for mathematics

Regularity in models of arithmetic. (English) Zbl 0584.03044
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.

03H15 Nonstandard models of arithmetic
03F30 First-order arithmetic and fragments
03C80 Logic with extra quantifiers and operators
03C62 Models of arithmetic and set theory
Full Text: DOI
[1] Logic Colloquium ’77 pp 199– (1978)
[2] Handbook of mathematical logic pp 1133– (1977)
[3] DOI: 10.1007/BFb0067653
[4] Some independence results for Peano arithmetic 43 pp 725– (1978) · Zbl 0408.03048
[5] DOI: 10.1007/BFb0090171
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.