16 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.  11
    A Descending Chain Condition for Groups Definable in o -Minimal Structures.Alessandro Berarducci, Margarita Otero, Yaa’cov Peterzil & Anand Pillay - 2005 - Annals of Pure and Applied Logic 134 (2):303-313.
    We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest type-definable subgroup G00 of bounded index and G/G00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author.
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  3.  3
    Intersection Theory for o-Minimal Manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.
    We develop an intersection theory for definable Cp-manifolds in an o-minimal expansion of a real closed field and we prove the invariance of the intersection numbers under definable Cp-homotopies . In particular we define the intersection number of two definable submanifolds of complementary dimensions, the Brouwer degree and the winding numbers. We illustrate the theory by deriving in the o-minimal context the Brouwer fixed point theorem, the Jordan-Brouwer separation theorem and the invariance of the Lefschetz numbers under definable Cp-homotopies. A. (...)
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  4.  12
    G-Linear Sets and Torsion Points in Definably Compact Groups.Margarita Otero & Ya’Acov Peterzil - 2009 - Archive for Mathematical Logic 48 (5):387-402.
    Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ${X \subseteq G}$ then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.
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  5.  15
    A Recursive Nonstandard Model of Normal Open Induction.Alessandro Berarducci & Margarita Otero - 1996 - Journal of Symbolic Logic 61 (4):1228-1241.
    Models of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.) In 1964 Shepherdson gave a recursive nonstandard model of open induction. His model is not normal and does not have any infinite prime elements. In this paper we present a recursive nonstandard model of normal open induction with an unbounded set of infinite prime elements.
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  6.  27
    Transfer Methods for o-Minimal Topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.
    Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from $\varphi^M$ to $\varphi^R$ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo-based on the work of A. Strzebonski-showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.
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  7.  48
    Corrigendum To: "Transfer Methods for O-Minimal Topology".Alessandro Berarducci, Mário Edmundo & Margarita Otero - 2007 - Journal of Symbolic Logic 72 (3):1079 - 1080.
  8.  8
    Locally Definable Homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.
    In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...)
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  9.  7
    The Joint Embedding Property in Normal Open Induction.Margarita Otero - 1993 - Annals of Pure and Applied Logic 60 (3):275-290.
    The models of normal open induction are those discretely ordered rings, integrally closed in their fraction field whose nonnegative part satisfy Peano's induction axioms for open formulas in the language of ordered semirings.It is known that neither open induction nor the usually studied stronger fragments of arithmetic , have the joint embedding property.We prove that normal models of open induction have the joint embedding property.
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  10.  7
    On Diophantine Equations Solvable in Models of Open Induction.Margarita Otero - 1990 - Journal of Symbolic Logic 55 (2):779-786.
    We consider IOpen, the subsystem of PA (Peano Arithmetic) with the induction scheme restricted to quantifier-free formulas. We prove that each model of IOpen can be embedded in a model where the equation x 2 1 + x 2 2 + x 2 3 + x 2 4 = a has a solution. The main lemma states that there is no polynomial f(x,y) with coefficients in a (nonstandard) DOR M such that $|f(x,y)| for every (x,y) ∈ C, where C is (...)
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  11.  14
    Corrigendum: On Diophantine Equations Solvable in Models of Open Induction.Margarita Otero - 1991 - Journal of Symbolic Logic 56 (3):811-812.
  12.  16
    Quadratic Forms in Normal Open Induction.Margarita Otero - 1993 - Journal of Symbolic Logic 58 (2):456-476.
    Models of normal open induction (NOI) are those discretely ordered rings, integrally closed in their fraction field whose nonnegative part satisfy Peano's induction axioms for open formulas in the language of ordered semirings. Here we study the problem of representability of an element a of a model M of NOI (in some extension of M) by a quadratic form of the type X2 + bY2 where b is a nonzero integer. Using either a trigonometric or a hyperbolic parametrization we prove (...)
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  13.  8
    Corrigendum: On Diophantine Equations Solvable in Models of Open Induction.Margarita Otero - 1991 - Journal of Symbolic Logic 56 (3):811.
  14.  11
    Generic Models of the Theory of Normal ${\Bf Z}$-Rings.Margarita Otero - 1992 - Notre Dame Journal of Formal Logic 33 (3):322-331.
  15.  8
    Preface.Joan Bagaria, Yiannis Moschovakis, Margarita Otero & Ivan Soskov - 2011 - Annals of Pure and Applied Logic 162 (7):489.
  16.  13
    The Amalgamation Property in Normal Open Induction.Margarita Otero - 1992 - Notre Dame Journal of Formal Logic 34 (1):50-55.