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Special Model Axiom in Nonstandard Set Theory
Author(s) -
Kanovei Vladimir,
Reeken Michael
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450308
Subject(s) - zermelo–fraenkel set theory , mathematics , axiom of choice , axiom , consistency (knowledge bases) , mathematical economics , urelement , set theory , constructive set theory , model theory , natural number , set (abstract data type) , discrete mathematics , calculus (dental) , computer science , geometry , medicine , dentistry , programming language
We demonstrate that the special model axiom SMA of Ross admits a natural formalization in Kawai's nonstandard set theory KST but is independent of KST. As an application of our methods to classical model theory, we present a short proof of the consistency (with ZFC) of the existence of a k + like k ‐saturated model of PA for a given cardinal k .