Structure theorems for o-minimal expansions of groups
نویسندگان
چکیده
منابع مشابه
Structure Theorems for o-Minimal Expansions of Groups
In this study the structure for O-minimal expansions of groups is considered Let be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) is semibounded, (2) has no poles, (3) cannot define a real closed field with domain R and order <, (4) is eventually linear and (5) every –definable set is a finit u...
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Let R be an o-minimal expansion of a divisible ordered abelian group (R, <, +, 0, 1) with a distinguished positive element 1. Then the following dichotomy holds: Either there is a 0-definable binary operation · such that (R, <, +, ·, 0, 1) is an ordered real closed field; or, for every definable function f : R → R there exists a 0-definable λ ∈ {0} ∪ Aut(R, +) with limx→+∞[f(x) − λ(x)] ∈ R. Thi...
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We study sets and groups definable in tame expansions of ominimal structures. Let M̃ = ⟨M, P ⟩ be an expansion of an o-minimal Lstructure M by a dense set P . We impose three tameness conditions on M̃ and prove a cone decomposition theorem for definable sets and functions in the realm of the o-minimal semi-bounded structures. The proof involves induction on the notion of ‘large dimension’ for def...
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We will calculate completely the Grothendieck rings, in the sense of first order logic, of o-minimal expansions of ordered abelian groups by introducing the notion of the bounded Euler characteristic.
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Suppose that G is a definably connected, definable group in an ominimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism p̃ : G̃ −→ G is a locally definable covering homomorphism and π1(G) is isomorphic to the o-minimal fundamental group π(G) of G defined using locally definable covering homomorphisms. ∗With partial support from the FCT (Fundação para a Ci...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2000
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(99)00043-3