CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES

Karel Hrbacek; Mikhail G. Katz

doi:10.1017/bsl.2022.43

CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES

Karel Hrbacek, Mikhail G. Katz

Department of Mathematics

City University of New York

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets. We show that internal frameworks provide successful accounts of nonstandard hulls and Loeb measures. The basic fact this work relies on is that the ultrapower of the standard universe by a standard ultrafilter is naturally isomorphic to a subuniverse of the internal universe.

Original language	English
Pages (from-to)	97-127
Number of pages	31
Journal	Bulletin of Symbolic Logic
Volume	29
Issue number	1
DOIs	https://doi.org/10.1017/bsl.2022.43
State	Published - 14 Mar 2023

Bibliographical note

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

Keywords

26E35

Access to Document

10.1017/bsl.2022.43

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CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES

Abstract

Bibliographical note

Keywords

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