8 found
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  1.  12
    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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  2.  14
    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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  3.  94
    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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  4.  4
    Generic Derivations on o-Minimal Structures.Antongiulio Fornasiero & Elliot Kaplan - 2020 - Journal of Mathematical Logic 21 (2):2150007.
    Let T be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language L. We study derivations δ on models ℳ⊧T. We introduce the no...
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  5.  11
    O-Minimal Cohomology: Finiteness and Invariance Results.Alessandro Berarducci & Antongiulio Fornasiero - 2009 - Journal of Mathematical Logic 9 (2):167-182.
    The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated (...)
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  6.  12
    Definably Connected Nonconnected Sets.Antongiulio Fornasiero - 2012 - Mathematical Logic Quarterly 58 (1):125-126.
    We give an example of a structure equation image on the real line, and a manifold M definable in equation image, such that M is definably connected but is not connected.
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  7.  7
    A Fundamental Dichotomy for Definably Complete Expansions of Ordered Fields.Antongiulio Fornasiero & Philipp Hieronymi - 2015 - Journal of Symbolic Logic 80 (4):1091-1115.
  8.  5
    Arithmetic of Dedekind Cuts of Ordered Abelian Groups.Antongiulio Fornasiero & Marcello Mamino - 2008 - Annals of Pure and Applied Logic 156 (2):210-244.
    We study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures.
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