Internal Approach to External Sets and Universes: Part 2. External Universes over the Universe of Bounded Set Theory

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Studia Logica 55 (3):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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10.1007/bf01057803

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Citations of this work

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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References found in this work

Standard foundations for nonstandard analysis.David Ballard & Karel Hrbacek - 1992 - Journal of Symbolic Logic 57 (2):741-748.

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