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Geometric Stability Theory
Introduction 1. Stability theory 2. The classical finite rank theory 3. Quasi finite axiomatizability 4. 1-based theories and groups 5. Groups and geometries 6. Unidimensional theories 7. RegularExpand
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Generic Structures and Simple Theories
TLDR
We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. Expand
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On groups and fields definable in o-minimal structures
The structure M = (M, <, R1, R2,…) is o-minimal if every definable set X ⊂ M is a finite union of intervals (a, b) and points. Let G be a group definable in M (i.e. G is a definable subset of Mn andExpand
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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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Jet spaces of varieties over differential and difference fields
Abstract We prove some new structural results on finite-dimensional differential algebraic varieties and difference algebraic varieties in characteristic zero, using elementary methods involving jetExpand
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DEFINABLE SETS IN ORDERED STRUCTURES. I
This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the ¢minimal structures. The definition of this class and the corresponding class of theories, theExpand
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Weakly normal groups
TLDR
We show that a group G is weakly normal if and only if every definable X ⊂ G n is a Boolean combination of cosets of acl (ϕ)-definable subgroups (of G n ) ∀n. Expand
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On NIP and invariant measures
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [13]. Among key results areExpand
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Simple Theories
TLDR
We show that any theory equipped with a notion of independence satisfying all the basic algebraic axioms, together with the Independence Theorem over a model, must be simple, and that moreover the notion of Independence must coincide with nonforking. Expand
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Model theory of fields
The model theory of fields is an area for important interactions between mathematical, logical and classical mathematics. Recently, there have been major applications of model theoretic ideas to realExpand
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