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Groups, measures, and the NIP
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’sExpand
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Definability of restricted theta functions and families of abelian varieties
We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure $\Rae$. In particular, weExpand
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Definable Compactness and Definable Subgroups of o‐Minimal Groups
The paper introduces the notion of definable compactness and within the context of o-minimal structures proves several topological properties of definably compact spaces. In particular a definableExpand
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A trichotomy theorem for o-minimal structures
Let M ˆ kM; <; . . . l be a linearly ordered structure. We de®ne M to be o-minimal if every de®nable subset of M is a ®nite union of intervals. Classical examples are ordered divisible abelian groupsExpand
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Definably simple groups in o-minimal structures
Let G = 〈G, ·〉 be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure 〈G, ·〉 (while definable means definable in the structure M). AssumeExpand
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Linear O-minimal structures
AbstractA linearly ordered structure $$\mathcal{M} = (M,< , \cdot \cdot \cdot )$$ is called o-minimal if every definable subset ofM is a finite union of points and intervals. Such an $$\mathcal{M}$$Expand
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Quasi-o-minimal structures
We develop a technique to investigate quasi-o-minimality and use it to study quasi-O-minimal ordered groups (possibly with extra structure). Expand
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On Groups and Rings Definable In O–Minimal Expansions of Real Closed Fields
Let 〈R,<,+, ·〉 be a real closed field and let M be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in M. We show that every M-definable ringExpand
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Generic sets in definably compact groups
A subset X of a group G is called left-generic if finitely many left-translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ GExpand
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Abstract In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. UnderExpand
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