Internal Approach to External Sets and Universes: Part 3: Partially Saturated Universes

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Studia Logica 56 (3):293-322 (1996)
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Abstract

In this article ‡ we show how the universe of HST, Hrbaček set theory admits a system of subuniverses which keep the Replacement, model Power set and Choice, and also keep as much of Saturation as it is necessary. This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.

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10.1007/bf00372770

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Review: Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 1. Bounded Set Theory; Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 2. External Universe over the Universe of Bounded Set Theory; Vladimir Kanovei, Michael Reeken, Internal Approach to External Sets and Universes. Part 3. Partially Saturated Universes. [REVIEW]Karel Hrbacek - 1999 - Journal of Symbolic Logic 64 (3):1365-1366.
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Citations of this work

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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References found in this work

Standard foundations for nonstandard analysis.David Ballard & Karel Hrbacek - 1992 - Journal of Symbolic Logic 57 (2):741-748.
Nonstandard set theory.Peter Fletcher - 1989 - Journal of Symbolic Logic 54 (3):1000-1008.

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