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2016 SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures
Jafar S. Eivazloo, Somayyeh Tari
Notre Dame J. Formal Logic 57(3): 399-410 (2016). DOI: 10.1215/00294527-3507270

Abstract

Continuous extension (CE) cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property (OCP) in those structures. Here, we define strong CE-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has SCE-cell decomposition if and only if its canonical o-minimal extension has CE-cell decomposition. Then, we show that every weakly o-minimal structure with SCE-cell decomposition satisfies OCP. Our last result implies that every o-minimal structure in which every definable open set is a union of finitely many open CE-cells, has CE-cell decomposition.

Citation

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Jafar S. Eivazloo. Somayyeh Tari. "SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures." Notre Dame J. Formal Logic 57 (3) 399 - 410, 2016. https://doi.org/10.1215/00294527-3507270

Information

Received: 14 March 2013; Accepted: 13 May 2014; Published: 2016
First available in Project Euclid: 20 April 2016

zbMATH: 1348.03034
MathSciNet: MR3521489
Digital Object Identifier: 10.1215/00294527-3507270

Subjects:
Primary: 03C64

Rights: Copyright © 2016 University of Notre Dame

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Vol.57 • No. 3 • 2016
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