Journal of Symbolic Logic 69 (1):165-182 (2004)

Abstract
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

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Consistency Results About Ordinal Definability.Kenneth McAloon - 1971 - Annals of Mathematical Logic 2 (4):449.
Realism, Nonstandard Set Theory, and Large Cardinals.Karel Hrbacek - 2001 - Annals of Pure and Applied Logic 109 (1-2):15-48.

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Citations of this work BETA

A Definable Nonstandard Enlargement.Frederik Herzberg - 2008 - Mathematical Logic Quarterly 54 (2):167-175.
A Theory of Hyperfinite Sets.P. V. Andreev & E. I. Gordon - 2006 - Annals of Pure and Applied Logic 143 (1-3):3-19.

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