Journal of Symbolic Logic

Standard sets in nonstandard set theory

Petr Andreev and Karel Hrbacek

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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.

Article information

Source
J. Symbolic Logic, Volume 69, Issue 1 (2004), 165-182.

Dates
First available in Project Euclid: 2 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1080938835

Digital Object Identifier
doi:10.2178/jsl/1080938835

Mathematical Reviews number (MathSciNet)
MR2039355

Zentralblatt MATH identifier
1067.03071

Keywords
Nonstandard set theory standardization ultraproduct elementary embedding

Citation

Andreev, Petr; Hrbacek, Karel. Standard sets in nonstandard set theory. J. Symbolic Logic 69 (2004), no. 1, 165--182. doi:10.2178/jsl/1080938835. https://projecteuclid.org/euclid.jsl/1080938835


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