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  1. Expansions of dense linear orders with the intermediate value property.Chris Miller - 2001 - Journal of Symbolic Logic 66 (4):1783-1790.
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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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  • Dimensions, matroids, and dense pairs of first-order structures.Antongiulio Fornasiero - 2011 - Annals of Pure and Applied Logic 162 (7):514-543.
    A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of Lascar U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding an integral domain, while not pregeometric in general, do have a unique existential matroid. Generalising previous results by van den Dries, we define dense elementary pairs of structures expanding an (...)
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  • Tame Topology and O-Minimal Structures.Lou van den Dries - 2000 - Bulletin of Symbolic Logic 6 (2):216-218.
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  • Definably complete structures are not pseudo-enumerable.Antongiulio Fornasiero - 2011 - Archive for Mathematical Logic 50 (5-6):603-615.
    We prove that a definably complete expansion of a field cannot be the image of a definable discrete set under a definable function.
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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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  • A Question of Van Den Dries and a Theorem of Lipshitz and Robinson; Not Everything Is Standard.Ehud Hrushovski & Ya'acov Peterzil - 2007 - Journal of Symbolic Logic 72 (1):119 - 122.
    We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.
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