WorldCat Identities

Hrushovski, Ehud 1959-

Works: 9 works in 52 publications in 2 languages and 1,547 library holdings
Roles: Author, Opponent, 958
Publication Timeline
Most widely held works by Ehud Hrushovski
Non-archimedean tame topology and stably dominated types by Ehud Hrushovski( )

15 editions published between 2016 and 2017 in English and held by 947 WorldCat member libraries worldwide

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections
Finite structures with few types by Gregory L Cherlin( Book )

13 editions published between 2003 and 2008 in English and held by 339 WorldCat member libraries worldwide

This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory
Stable domination and independence in algebraically closed valued fields by Deirdre Haskell( Book )

15 editions published between 2007 and 2011 in English and held by 245 WorldCat member libraries worldwide

"This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory."
Contributions to stable model theory by Ehud Hrushovski( )

4 editions published in 1986 in English and held by 7 WorldCat member libraries worldwide

Stable Domination and Independence in Algebraically Closed Valued Fields. Lecture Notes in Logic, Volume 30( )

1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide

This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part
ICM '98 : International Congress of Mathematicians, August 18-27, 1998, Berlin by International Congress of Mathematicians( Book )

1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide

Groupes et Corps dans des Théories Neostables : condition de Chaîne et Enveloppes Définissables by Nadja Hempel( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

This thesis is dedicated to the study of groups and fields whose definable sets do not admit certain combinatorial patterns. Given a group G, one particular problem we are interested in is to find definable envelopes for arbitrary abelian, nilpotent or solvable subgroups of G which admit the same algebraic properties. Such evelopes exists if G is stable and even if G is merely dependent but sufficiently saturated, with the additional hypothesis of normality in the solvable case. In groups with a simple theory, one obtains definable envelopes up to finite index.We introduce the notion of an almost centralizer and establish some of its basic properties. This enables us to extend the aforementioned results to Mc~ groups, i. e. groups in which any definable section satisfies a chain condition on centralizers up to finite index. These include any definable group in a rosy and in particular in a simple theory. Furthermore, inspired from the proof in dependent theories as well as using techniques developed for almost centralizers in this thesis, we are able to find definable envelopes up to finite index for abelian, nilpotent and normal solvable subgroups of any enough saturated NTP2 group. Moreover, using envelopes for nilpotent subgroups of Mc~ groups and the chain condition on centralizer up to finite index, we show additionally that the Fitting subgroup of any Mc~ group is nilpotent and that its almost Fitting subgroup is virtually solvable.The second part of this thesis focuses on the study of n-dependent fields. We prove that any n-dependent field is Artin-Schreier closed and that non separably closed PAC fields are not n-dependent for any natural number n
Flots géodésiques et théorie des modèles des corps différentiels by Rémi Jaoui( )

1 edition published in 2017 in French and held by 1 WorldCat member library worldwide

This thesis is dedicated to studying the interactions between two different approaches regarding differential equations: the model-theory of differentially closed fields on the one side and the dynamical analysis of real differential equations, on the other side. In the first chapter, we present a formalism from differential algebra, in terms of D-varieties à la Buium over the field of real numbers (endowed with the trivial derivation), that allows one to realise both approaches at the same time. The main result is a criterion of orthogonality to the constants, based on the topological dynamic of its associated real analytic flow. The second chapter is dedicated to the algebraic differential equations describing the (unitary) geodesic flow of a real algebraic variety endowed with an algebraic, non-degenerated symmetric 2-form. Using the previous criterion, we prove a theorem of orthogonality to the constants "in negative curvature'', that relies on the results of Anosov and of his followers, regarding the topological dynamic - the weakly mixing topological property - for the geodesic flow of a compact Riemannian manifold with negative curvature. In dimension 2, we conjecture a more precise description - its generic type is minimal and has a trivial pregeometry- for the structure associated to the unitary geodesic equation. In the third chapter, we present some motivations and partial results on this conjecture
Ordre et stabilité dans les théories NIP by Pierre Simon( )

1 edition published in 2011 in French and held by 1 WorldCat member library worldwide

This thesis deals with model theory, a branch of mathematical logic.We study a particular class of theories called "NIP theories", which includes in particular some ordered fields and valued fields. We are interested in various aspects of those structures. First, we study a specific class of measures, which we call "generically stable measures". We show that they have properties analogous to those of types in a stable theory and we give some constructions to produce them. We also study a weak form of definability of types. Finally, we define a notion of a "purely unstable" NIP theory and show how, in general, we can detect the stable parts of types
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.37 (from 0.18 for Non-archim ... to 0.99 for Flots géo ...)

Finite structures with few types
Stable domination and independence in algebraically closed valued fields
Alternative Names
Ehud Hrushovski

Ehud Hrushovski Israeli mathematician

Ehud Hrushovski israelischer Mathematiker

Ehud Hrushovski matemático israelí

Ehud Hrushovski mathématicien israélien

Ehud Hrushovski wiskundige uit Israël

Эхуд Хрушовски математик

הרושאווסקי, אהוד

에후드 흐루쇼프스키


English (50)

French (2)