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
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| Keywords | Nonstandard set theory standardization ultraproduct elementary embedding |
| Categories | (categorize this paper) |
| 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.
A Nonstandard Set Theory in the $\displaystyle\in$ -Language.Vladimir Kanovei & Michael Reeken - 2000 - Archive for Mathematical Logic 39 (6):403-416.
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.
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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