arXiv Open Access 2023

Constructing nonstandard hulls and Loeb measures in internal set theories

Karel Hrbacek Mikhail G. Katz

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Abstrak

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.

Topik & Kata Kunci

math.LO math.CA

Penulis (2)

Karel Hrbacek

Mikhail G. Katz

Format Sitasi

APA MLA BibTeX

Hrbacek, K., Katz, M.G. (2023). Constructing nonstandard hulls and Loeb measures in internal set theories. https://arxiv.org/abs/2301.00367

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓