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
Karel Hrbacek (2001). Realism, Nonstandard Set Theory, and Large Cardinals. Annals of Pure and Applied Logic 109 (1-2):15-48.

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

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