8 found
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  1.  10
    Definably Compact Abelian Groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
  2.  5
    A Remark on Divisibility of Definable Groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.
    We show that if G is a definably compact, definably connected definable group defined in an arbitrary o-minimal structure, then G is divisible. Furthermore, if G is defined in an o-minimal expansion of a field, k ∈ ℕ and pk : G → G is the definable map given by pk = xk for all x ∈ G , then we have |–1| ≥ kr for all x ∈ G , where r > 0 is the maximal dimension of abelian (...)
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  3.  15
    Structure Theorems for o-Minimal Expansions of Groups.Mario J. Edmundo - 2000 - Annals of Pure and Applied Logic 102 (1-2):159-181.
    Let R be an o-minimal expansion of an ordered group R has no poles, R cannot define a real closed field with domain R and order R is eventually linear and every R -definable set is a finite union of cones. As a corollary we get that Th has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R -definable sets and a symbol for each definable endomorphism of the group.
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  4.  23
    Sheaf Cohomology in o-Minimal Structures.Mário J. Edmundo, Gareth O. Jones & Nicholas J. Peatfield - 2006 - Journal of Mathematical Logic 6 (2):163-179.
  5.  19
    The Universal Covering Homomorphism in o‐Minimal Expansions of Groups.Mário J. Edmundo & Pantelis E. Eleftheriou - 2007 - Mathematical Logic Quarterly 53 (6):571-582.
    Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism equation image: equation image→ G is a locally definable covering homomorphism and π1 is isomorphic to the o-minimal fundamental group π of G defined using locally definable covering homomorphisms.
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  6.  14
    Coverings by Open Cells.Mário J. Edmundo, Pantelis E. Eleftheriou & Luca Prelli - 2014 - Archive for Mathematical Logic 53 (3-4):307-325.
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  7.  42
    Invariance Results for Definable Extensions of Groups.Mário J. Edmundo, Gareth O. Jones & Nicholas J. Peatfield - 2011 - Archive for Mathematical Logic 50 (1-2):19-31.
    We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.
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  8.  5
    On the Euler Characteristic of Definable Groups.Mário J. Edmundo - 2011 - Mathematical Logic Quarterly 57 (1):44-46.
    We show that in an arbitrary o-minimal structure the following are equivalent: conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; every infinite, definably connected, definably compact definable group has a non trivial torsion point.
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