Special Model Axiom in Nonstandard Set Theory | Zendy

Kanovei Vladimir | Zendy; Reeken Michael | Zendy

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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 .

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