Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 1 (2019), 61-76.
Tame Topology over dp-Minimal Structures
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.
Notre Dame J. Formal Logic, Volume 60, Number 1 (2019), 61-76.
Received: 1 November 2015
Accepted: 15 November 2016
First available in Project Euclid: 16 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 03C68: Other classical first-order model theory
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