Hrushovski, Ehud 1959
Overview
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
Nonarchimedean 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 ominimality, providing finiteness and uniformity statements and new structural tools. For nonarchimedean fields, such as the padics, 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 modeltheoretic foundations for nonarchimedean geometry. The methods combine ominimality 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 nonarchimedean 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 nonarchimedean geometry is assumed. Modeltheoretic prerequisites are reviewed in the first sections
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 ominimality, providing finiteness and uniformity statements and new structural tools. For nonarchimedean fields, such as the padics, 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 modeltheoretic foundations for nonarchimedean geometry. The methods combine ominimality 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 nonarchimedean 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 nonarchimedean geometry is assumed. Modeltheoretic 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 4tuples. 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
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 4tuples. 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 modeltheoretic 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."
15 editions published between 2007 and 2011 in English and held by 245 WorldCat member libraries worldwide
"This book addresses a gap in the modeltheoretic 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
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 modeltheoretic 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
1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
This book addresses a gap in the modeltheoretic 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 1827, 1998, Berlin by International Congress of Mathematicians(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
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 ndependent fields. We prove that any ndependent field is ArtinSchreier closed and that non separably closed PAC fields are not ndependent for any natural number n
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 ndependent fields. We prove that any ndependent field is ArtinSchreier closed and that non separably closed PAC fields are not ndependent 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 modeltheory 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 Dvarieties 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, nondegenerated symmetric 2form. 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
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 modeltheory 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 Dvarieties 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, nondegenerated symmetric 2form. 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
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
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Related Identities
 Loeser, François
 Cherlin, Gregory L. 1948 Author
 Macpherson, Dugald
 Haskell, Deirdre 1963 Author
 Association for Symbolic Logic
 Bouscaren, Élisabeth (1956....). Opponent Thesis advisor
 Université ParisSud Degree grantor
 Bost, JeanBenoît (1961....). Opponent Thesis advisor
 Laboratoire de Mathématiques d'Orsay
 Université ParisSaclay Degree grantor
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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
エウド・フルショフスキー
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