Locally o-minimal structures and structures with locally o-minimal open core

Annals of Pure and Applied Logic 164 (3):211-229 (2013)
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Abstract

We study first-order expansions of ordered fields that are definably complete, and moreover either are locally o-minimal, or have a locally o-minimal open core. We give a characterisation of structures with locally o-minimal open core, and we show that dense elementary pairs of locally o-minimal structures have locally o-minimal open core

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10.1016/j.apal.2012.10.002

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Citations of this work

Locally o-Minimal Structures with Tame Topological Properties.Masato Fujita - 2023 - Journal of Symbolic Logic 88 (1):219-241.
Almost o-minimal structures and X -structures.Masato Fujita - 2022 - Annals of Pure and Applied Logic 173 (9):103144.
O-minimalism.Hans Schoutens - 2014 - Journal of Symbolic Logic 79 (2):355-409.

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References found in this work

Notes on local o‐minimality.Carlo Toffalori & Kathryn Vozoris - 2009 - Mathematical Logic Quarterly 55 (6):617-632.
Dimensions, matroids, and dense pairs of first-order structures.Antongiulio Fornasiero - 2011 - Annals of Pure and Applied Logic 162 (7):514-543.
Tame Topology and O-Minimal Structures.Lou van den Dries - 2000 - Bulletin of Symbolic Logic 6 (2):216-218.
Definably complete structures are not pseudo-enumerable.Antongiulio Fornasiero - 2011 - Archive for Mathematical Logic 50 (5-6):603-615.

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