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Standard sets in nonstandard set theory

Published online by Cambridge University Press:  12 March 2014

Petr Andreev  and
Karel Hrbacek
Petr Andreev
Affiliation:
1106-563 Zelenograd, Moscow 124460, Russia, E-mail: petr@heptachor.ru
Karel Hrbacek
Affiliation:
Department of Mathematics, City College of Cuny, New York, NY 10031, USA, E-mail: khrbacek@ccny.cuny.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 1 , March 2004 , pp. 165 - 182
Copyright
Copyright © Association for Symbolic Logic 2004

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