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  1. Locally o-minimal structures and structures with locally o-minimal open core.Antongiulio Fornasiero - 2013 - Annals of Pure and Applied Logic 164 (3):211-229.
    We study first-order expansions of ordered fields that are definably complete, and moreover either are locally o-minimal, or have a locally o-minimal open core. We give a characterisation of structures with locally o-minimal open core, and we show that dense elementary pairs of locally o-minimal structures have locally o-minimal open core.
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  • Open core and small groups in dense pairs of topological structures.Elías Baro & Amador Martin-Pizarro - 2021 - Annals of Pure and Applied Logic 172 (1):102858.
    Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to (...)
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