CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES

Karel Hrbacek, Mikhail G. Katz

Research output: Contribution to journalArticlepeer-review

1 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 languageEnglish
Pages (from-to)97-127
Number of pages31
JournalBulletin of Symbolic Logic
Volume29
Issue number1
DOIs
StatePublished - 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

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