Special Model Axiom in Nonstandard Set Theory

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Mathematical Logic Quarterly 45 (3):371-384 (1999)
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Abstract

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 of the existence of a k+ like k-saturated model of PA for a given cardinal k

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10.1002/malq.19990450308

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References found in this work

Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.
The isomorphism property versus the special model axiom.Renling Jin - 1992 - Journal of Symbolic Logic 57 (3):975-987.
The special model axiom in nonstandard analysis.David Ross - 1990 - Journal of Symbolic Logic 55 (3):1233-1242.
Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.

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