Author: Anand Pillay
Publisher: Oxford University Press on Demand
ISBN: 9780198534372
Category : Language Arts & Disciplines
Languages : en
Pages : 361
Book Description
This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine structure of models of stable theories. An ever present theme is the existence and structure of definable groups.Fundamental applications to a classification theory are included in the text. Recent years have seen other surprising applications to, among other things, diophantine geometry. This book will be invaluable to anyone interested in modern model theory, such as working model theorists and graduatestudents in logic.
Geometric Stability Theory
Author: Anand Pillay
Publisher: Oxford University Press on Demand
ISBN: 9780198534372
Category : Language Arts & Disciplines
Languages : en
Pages : 361
Book Description
This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine structure of models of stable theories. An ever present theme is the existence and structure of definable groups.Fundamental applications to a classification theory are included in the text. Recent years have seen other surprising applications to, among other things, diophantine geometry. This book will be invaluable to anyone interested in modern model theory, such as working model theorists and graduatestudents in logic.
Publisher: Oxford University Press on Demand
ISBN: 9780198534372
Category : Language Arts & Disciplines
Languages : en
Pages : 361
Book Description
This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine structure of models of stable theories. An ever present theme is the existence and structure of definable groups.Fundamental applications to a classification theory are included in the text. Recent years have seen other surprising applications to, among other things, diophantine geometry. This book will be invaluable to anyone interested in modern model theory, such as working model theorists and graduatestudents in logic.
Geometric Theory of Dynamical Systems
Author: J. Jr. Palis
Publisher: Springer Science & Business Media
ISBN: 1461257034
Category : Mathematics
Languages : en
Pages : 208
Book Description
... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.
Publisher: Springer Science & Business Media
ISBN: 1461257034
Category : Mathematics
Languages : en
Pages : 208
Book Description
... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.
Fundamentals of Stability Theory
Author: John T. Baldwin
Publisher: Cambridge University Press
ISBN: 1107168090
Category : Mathematics
Languages : en
Pages : 462
Book Description
This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
Publisher: Cambridge University Press
ISBN: 1107168090
Category : Mathematics
Languages : en
Pages : 462
Book Description
This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
Classification Theory
Author: S. Shelah
Publisher: Elsevier
ISBN: 008088024X
Category : Computers
Languages : en
Pages : 741
Book Description
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m
Publisher: Elsevier
ISBN: 008088024X
Category : Computers
Languages : en
Pages : 741
Book Description
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m
Hydrodynamic stability theory
Author: A. Georgescu
Publisher: Springer Science & Business Media
ISBN: 9401718148
Category : Mathematics
Languages : en
Pages : 306
Book Description
The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.
Publisher: Springer Science & Business Media
ISBN: 9401718148
Category : Mathematics
Languages : en
Pages : 306
Book Description
The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.
Model Theory and Algebraic Geometry
Author: Elisabeth Bouscaren
Publisher: Springer
ISBN: 3540685219
Category : Mathematics
Languages : en
Pages : 223
Book Description
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Publisher: Springer
ISBN: 3540685219
Category : Mathematics
Languages : en
Pages : 223
Book Description
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Geometric Shell Stability Theory
Author: A. V. Pogorelov
Publisher:
ISBN:
Category :
Languages : en
Pages : 465
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 465
Book Description
Geometric Theory of Discrete Nonautonomous Dynamical Systems
Author: Christian Pötzsche
Publisher: Springer Science & Business Media
ISBN: 3642142575
Category : Mathematics
Languages : en
Pages : 422
Book Description
The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Publisher: Springer Science & Business Media
ISBN: 3642142575
Category : Mathematics
Languages : en
Pages : 422
Book Description
The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Geometric Theory of Semilinear Parabolic Equations
Author: Daniel Henry
Publisher: Springer
ISBN: 3540385282
Category : Mathematics
Languages : en
Pages : 353
Book Description
Publisher: Springer
ISBN: 3540385282
Category : Mathematics
Languages : en
Pages : 353
Book Description
Model Theory, Algebra, and Geometry
Author: Deirdre Haskell
Publisher: Cambridge University Press
ISBN: 9780521780681
Category : Mathematics
Languages : en
Pages : 244
Book Description
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Publisher: Cambridge University Press
ISBN: 9780521780681
Category : Mathematics
Languages : en
Pages : 244
Book Description
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.