Internal approach to external sets and universes

Studia Logica 55 (2):347 - 376 (1995)

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Abstract
In this article we show how the universe of BST, bounded set theory can be enlarged by definable subclasses of sets so that Separation and Replacement are true in the enlargement for all formulas, including those in which the standardness predicate may occur. Thus BST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop topics in nonstandard analysis inaccessible in the framework of a purely internal approach, such as Loeb measures
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DOI 10.1007/BF00372770
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References found in this work BETA

Standard Foundations for Nonstandard Analysis.David Ballard & Karel Hrbacek - 1992 - Journal of Symbolic Logic 57 (2):741-748.
On the Strength of Nonstandard Analysis.C. Ward Henson & H. Jerome Keisler - 1986 - Journal of Symbolic Logic 51 (2):377-386.
Nonstandard Set Theory.Peter Fletcher - 1989 - Journal of Symbolic Logic 54 (3):1000-1008.
Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.

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Citations of this work BETA

A Definable Nonstandard Enlargement.Frederik Herzberg - 2008 - Mathematical Logic Quarterly 54 (2):167-175.
Special Model Axiom in Nonstandard Set Theory.Vladimir Kanovei & Michael Reeken - 1999 - Mathematical Logic Quarterly 45 (3):371-384.

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