Notre Dame Journal of Formal Logic

Tame Topology over dp-Minimal Structures

Pierre Simon and Erik Walsberg

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Abstract

In this article, we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multivalued functions.” This generalizes known statements about weakly o-minimal, C-minimal, and P-minimal theories.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 1 (2019), 61-76.

Dates
Received: 1 November 2015
Accepted: 15 November 2016
First available in Project Euclid: 16 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1547607904

Digital Object Identifier
doi:10.1215/00294527-2018-0019

Mathematical Reviews number (MathSciNet)
MR3911106

Subjects
Primary: 03C68: Other classical first-order model theory

Keywords
dp-minimal o-minimal C-minimal tame topology

Citation

Simon, Pierre; Walsberg, Erik. Tame Topology over dp-Minimal Structures. Notre Dame J. Formal Logic 60 (2019), no. 1, 61--76. doi:10.1215/00294527-2018-0019. https://projecteuclid.org/euclid.ndjfl/1547607904


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References

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