Regularity in Models of Arithmetic

Mills, George; Paris, Jeff

J. Symbolic Logic, Tome 49 (1984) no. 1, p. 272-280 / Harvested from Project Euclid

Résumé

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.

Publié le : 1984-03-14
Classification:

@article{1183741493,
     author = {Mills, George and Paris, Jeff},
     title = {Regularity in Models of Arithmetic},
     journal = {J. Symbolic Logic},
     volume = {49},
     number = {1},
     year = {1984},
     pages = { 272-280},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741493}
}

Mills, George; Paris, Jeff. Regularity in Models of Arithmetic. J. Symbolic Logic, Tome 49 (1984) no. 1, pp.  272-280. http://gdmltest.u-ga.fr/item/1183741493/