6 found
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  1.  25
    Vector spaces with a union of independent subspaces.Alessandro Berarducci, Marcello Mamino & Rosario Mennuni - 2024 - Archive for Mathematical Logic 63 (3):499-507.
    We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.
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  2.  21
    Orthogonal Decomposition of Definable Groups.Alessandro Berarducci, Pantelis E. Eleftheriou & Marcello Mamino - 2024 - Journal of Symbolic Logic 89 (3):1158-1179.
    Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing the idea of interaction among all parts of a given definable set. A cohesive set is indecomposable, in the sense that if it is internal to the product of two orthogonal sets, then it is internal to one of the two. We prove that a definable group in an o-minimal structure is a product of cohesive orthogonal (...)
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  3.  30
    (1 other version)Asymptotic analysis of skolem’s exponential functions.Alessandro Berarducci & Marcello Mamino - 2020 - Journal of Symbolic Logic:1-25.
    Skolem studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function ${\mathbf {x}}$, and such that whenever f and g are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz computed the order type of the fragment below $2^{2^{\mathbf {x}}}$. Here we prove that (...)
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  4.  29
    Fundamental group in o-minimal structures with definable Skolem functions.Bruno Dinis, Mário J. Edmundo & Marcello Mamino - 2021 - Annals of Pure and Applied Logic 172 (8):102975.
    In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and prove that definably connected, locally definable manifolds are uniformly definably path connected, have an admissible cover by definably simply connected, open definable subsets and, definable paths and definable homotopies on such locally definable manifolds can be lifted to locally definable covering maps. These properties allow us to obtain the main properties of the general o-minimal fundamental group, including: invariance and comparison results; existence of universal locally (...)
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  5.  23
    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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  6.  39
    Splitting definably compact groups in o-minimal structures.Marcello Mamino - 2011 - Journal of Symbolic Logic 76 (3):973 - 986.
    An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.
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