## Works by Somayyeh Tari

6 found
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1. 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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2. Strong cell decomposition property in o-minimal traces.Somayyeh Tari - 2020 - 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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3. A note on prime models in weakly o‐minimal structures.Somayyeh Tari - 2017 - Mathematical Logic Quarterly 63 (1-2):109-113.
Let be a weakly o‐minimal structure with the strong cell decomposition property. In this note, we show that the canonical o‐minimal extension of is the unique prime model of the full first order theory of over any set. We also show that if two weakly o‐minimal structures with the strong cell decomposition property are isomorphic then, their canonical o‐minimal extensions are isomorphic too. Finally, we show the uniqueness of the prime models in a complete weakly o‐minimal theory with prime models.
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4. A criterion for the strong cell decomposition property.Somayyeh Tari - 2023 - Archive for Mathematical Logic 62 (7):871-887.
Let $${\mathcal {M}}=(M, <, \ldots )$$ be a weakly o-minimal structure. Assume that $${\mathcal {D}}ef({\mathcal {M}})$$ is the collection of all definable sets of $${\mathcal {M}}$$ and for any $$m\in {\mathbb {N}}$$, $${\mathcal {D}}ef_m({\mathcal {M}})$$ is the collection of all definable subsets of $$M^m$$ in $${\mathcal {M}}$$. We show that the structure $${\mathcal {M}}$$ has the strong cell decomposition property if and only if there is (...)
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5. SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures.Jafar S. Eivazloo & Somayyeh Tari - 2016 - Notre Dame Journal of Formal Logic 57 (3):399-410.
Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong $\mathrm{CE}$-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has $\mathrm{SCE}$-cell decomposition if and only if its canonical o-minimal extension has $\mathrm{CE}$-cell decomposition. Then, we show that every weakly o-minimal structure with $\mathrm{SCE}$-cell decomposition satisfies $\mathrm{OCP}$. Our last result implies that every o-minimal structure in which every definable open (...)