Standard sets in nonstandard set theory

Journal of Symbolic Logic 69 (1):165-182 (2004)
We prove that Standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the ∈-language
Keywords Nonstandard set theory   standardization   ultraproduct   elementary embedding
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DOI 10.2178/jsl/1080938835
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References found in this work BETA
Consistency Results About Ordinal Definability.Kenneth McAloon - 1971 - Annals of Mathematical Logic 2 (4):449-467.
Realism, Nonstandard Set Theory, and Large Cardinals.Karel Hrbacek - 2001 - Annals of Pure and Applied Logic 109 (1-2):15-48.
A Nonstandard Set Theory in the Displaystylein-Language.Vladimir Kanovei & Michael Reeken - 2000 - Archive for Mathematical Logic 39 (6):403-416.

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A Theory of Hyperfinite Sets.P. V. Andreev & E. I. Gordon - 2006 - Annals of Pure and Applied Logic 143 (1):3-19.

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