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  1. A Note on Prime Models in Weakly o‐Minimal Structures.Somayyeh Tari - 2017 - Mathematical Logic Quarterly 63 (1-2):109-113.
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  • Pseudo Definably Connected Definable Sets.Jafar S. Eivazloo & Somayyeh Tari - 2016 - Mathematical Logic Quarterly 62 (3):241-248.
    In o-minimal structures, every cell is definably connected and every definable set is a finite union of its definably connected components. In this note, we introduce pseudo definably connected definable sets in weakly o-minimal structures having strong cell decomposition, and prove that every strong cell in those structures is pseudo definably connected. It follows that every definable set can be written as a finite union of its pseudo definably connected components. We also show that the projections of pseudo definably connected (...)
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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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  • A Theory of Pairs for Non-Valuational Structures.Elitzur Bar-Yehuda, Assaf Hasson & Ya’Acov Peterzil - 2019 - Journal of Symbolic Logic 84 (2):664-683.
    Given a weakly o-minimal structure${\cal M}$and its o-minimal completion$\bar{{\cal M}}$, we first associate to$\bar{{\cal M}}$a canonical language and then prove thatTh$\left$determines$Th\left$. We then investigate the theory of the pair$\left$in the spirit of the theory of dense pairs of o-minimal structures, and prove, among other results, that it is near model complete, and every definable open subset of${\bar{M}^n}$is already definable in$\bar{{\cal M}}$.We give an example of a weakly o-minimal structure interpreting$\bar{{\cal M}}$and show that it is not elementarily equivalent to any reduct (...)
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  • On Definable Skolem Functions in Weakly o-Minimal Nonvaluational Structures.Pantelis E. Eleftheriou, Assaf Hasson & Gil Keren - 2017 - Journal of Symbolic Logic 82 (4):1482-1495.
    We prove that all known examples of weakly o-minimal nonvaluational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up to definable families of cuts. Along the way we give some new examples of weakly o-minimal nonvaluational structures.
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