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  1. Locally o-Minimal Structures with Tame Topological Properties.Masato Fujita - forthcoming - Journal of Symbolic Logic:1-23.
    We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.
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  • Almost o-Minimal Structures and X-Structures.Masato Fujita - 2022 - Annals of Pure and Applied Logic 173 (9):103144.
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  • Groups, Group Actions and Fields Definable in First‐Order Topological Structures.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (6):449-467.
    Given a group , G⊆Mm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V⊆G and define a new topology τ on G with which becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory facts concerning (...)
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  • On the Strong Cell Decomposition Property for Weakly o‐Minimal Structures.Roman Wencel - 2013 - Mathematical Logic Quarterly 59 (6):452-470.
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  • Strong cell decomposition property in o-minimal traces.Somayyeh Tari - 2021 - Archive for Mathematical Logic 60 (1):135-144.
    Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.
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  • Uniformly Locally o-Minimal Structures and Locally o-Minimal Structures Admitting Local Definable Cell Decomposition.Masato Fujita - 2020 - Annals of Pure and Applied Logic 171 (2):102756.
    We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...)
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  • Tame Properties of Sets and Functions Definable in Weakly o-Minimal Structures.Jafar S. Eivazloo & Somayyeh Tari - 2014 - Archive for Mathematical Logic 53 (3-4):433-447.
    Let M=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}=}$$\end{document} be a weakly o-minimal expansion of a dense linear order without endpoints. Some tame properties of sets and functions definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} which hold in o-minimal structures, are examined. One of them is the intermediate value property, say IVP. It is shown that strongly continuous definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} satisfy an extended (...)
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  • Heirs of Box Types in Polynomially Bounded Structures.Marcus Tressl - 2009 - Journal of Symbolic Logic 74 (4):1225 - 1263.
    A box type is an n-type of an o-minimal structure which is uniquely determined by the projections to the coordinate axes. We characterize heirs of box types of a polynomially bounded o-minimal structure M. From this, we deduce various structure theorems for subsets of $M^k $ , definable in the expansion M of M by all convex subsets of the line. We show that M after naming constants, is model complete provided M is model complete.
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