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  1. 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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  • Notes on local o‐minimality.Carlo Toffalori & Kathryn Vozoris - 2009 - Mathematical Logic Quarterly 55 (6):617-632.
    We introduce and study some local versions of o-minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions.
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