Author : Anand Pillay
Publisher : Unknown
Page : 0 pages
File Size : 51,6 Mb
Release : 2023
Category : Model theory
ISBN : 1383025304
Geometric Stability Theory
Anand Pillay
Geometric Stability Theory
Geometric Stability Theory Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Geometric Stability Theory book. This book definitely worth reading, it is an incredibly well-written.
Geometric Stability Theory
Anand Pillay,Professor of Mathematics Anand Pillay
Author : Anand Pillay,Professor of Mathematics Anand Pillay
Publisher : Oxford University Press on Demand
Page : 361 pages
File Size : 46,9 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 019853437X
Geometric Stability Theory by Anand Pillay,Professor of Mathematics Anand Pillay Pdf
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.
Essential Stability Theory
Steven Buechler
Author : Steven Buechler
Publisher : Cambridge University Press
Page : 368 pages
File Size : 50,8 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168398
Essential Stability Theory by Steven Buechler Pdf
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Stability theory was introduced and matured in the 1960s and 1970s. Today stability theory influences and is influenced by number theory, algebraic group theory, Riemann surfaces, and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. In this volume, the fourth publication in the Perspectives in Logic series, Steven Buechler bridges the gap between a first-year graduate logic course and research papers in stability theory. The book prepares the student for research in any of today's branches of stability theory, and gives an introduction to classification theory with an exposition of Morley's Categoricity Theorem.
Geometric Theory of Dynamical Systems
J. Jr. Palis,W. de Melo
Author : J. Jr. Palis,W. de Melo
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257035
Geometric Theory of Dynamical Systems by J. Jr. Palis,W. de Melo Pdf
... 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.
Classification Theory
S. Shelah
Author : S. Shelah
Publisher : Elsevier
Page : 740 pages
File Size : 55,8 Mb
Release : 1990-12-06
Category : Mathematics
ISBN : 008088024X
Classification Theory by S. Shelah Pdf
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|M|. This theorem is also the subject of Chapter XIII.
Model Theory and Algebraic Geometry
Elisabeth Bouscaren
Author : Elisabeth Bouscaren
Publisher : Springer
Page : 223 pages
File Size : 43,7 Mb
Release : 2009-03-14
Category : Mathematics
ISBN : 9783540685210
Model Theory and Algebraic Geometry by Elisabeth Bouscaren Pdf
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.
Fundamentals of Stability Theory
John T. Baldwin
Author : John T. Baldwin
Publisher : Cambridge University Press
Page : 462 pages
File Size : 50,7 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168091
Fundamentals of Stability Theory by John T. Baldwin Pdf
This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
Geometric Theory of Discrete Nonautonomous Dynamical Systems
Christian Pötzsche
Author : Christian Pötzsche
Publisher : Springer
Page : 422 pages
File Size : 42,9 Mb
Release : 2010-08-24
Category : Mathematics
ISBN : 9783642142581
Geometric Theory of Discrete Nonautonomous Dynamical Systems by Christian Pötzsche Pdf
Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal 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). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
Geometric Theory of Semilinear Parabolic Equations
Daniel Henry
Author : Daniel Henry
Publisher : Springer
Page : 353 pages
File Size : 40,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385288
Geometric Theory of Semilinear Parabolic Equations by Daniel Henry Pdf
Structural Stability Theory and Practice
Sukhvarsh Jerath
Author : Sukhvarsh Jerath
Publisher : John Wiley & Sons
Page : 674 pages
File Size : 51,9 Mb
Release : 2020-12-08
Category : Technology & Engineering
ISBN : 9781119694496
Structural Stability Theory and Practice by Sukhvarsh Jerath Pdf
Discover the theory of structural stability and its applications in crucial areas in engineering Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shells combines necessary information on structural stability into a single, comprehensive resource suitable for practicing engineers and students alike. Written in both US and SI units, this invaluable guide is perfect for readers within and outside of the US. Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell offers: Detailed and patiently developed mathematical derivations and thorough explanations Energy methods that are incorporated throughout the chapters Connections between theory, design specifications and solutions The latest codes and standards from the American Institute of Steel Construction (AISC), Canadian Standards Association (CSA), Australian Standards (SAA), Structural Stability Research Council (SSRC), and Eurocode 3 Solved and unsolved practice-oriented problems in every chapter, with a solutions manual for unsolved problems included for instructors Ideal for practicing professionals in civil, mechanical, and aerospace engineering, as well as upper-level undergraduates and graduate students in structural engineering courses, Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell provides readers with detailed mathematical derivations along with thorough explanations and practical examples.
Geometric Theory of Foliations
César Camacho,Alcides Lins Neto
Author : César Camacho,Alcides Lins Neto
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 55,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461252924
Geometric Theory of Foliations by César Camacho,Alcides Lins Neto Pdf
Intuitively, a foliation corresponds to a decomposition of a manifold into a union of connected, disjoint submanifolds of the same dimension, called leaves, which pile up locally like pages of a book. The theory of foliations, as it is known, began with the work of C. Ehresmann and G. Reeb, in the 1940's; however, as Reeb has himself observed, already in the last century P. Painleve saw the necessity of creating a geometric theory (of foliations) in order to better understand the problems in the study of solutions of holomorphic differential equations in the complex field. The development of the theory of foliations was however provoked by the following question about the topology of manifolds proposed by H. Hopf in the 3 1930's: "Does there exist on the Euclidean sphere S a completely integrable vector field, that is, a field X such that X· curl X • 0?" By Frobenius' theorem, this question is equivalent to the following: "Does there exist on the 3 sphere S a two-dimensional foliation?" This question was answered affirmatively by Reeb in his thesis, where he 3 presents an example of a foliation of S with the following characteristics: There exists one compact leaf homeomorphic to the two-dimensional torus, while the other leaves are homeomorphic to two-dimensional planes which accu mulate asymptotically on the compact leaf. Further, the foliation is C"".
Finite Structures with Few Types
Gregory L. Cherlin,Ehud Hrushovski
Author : Gregory L. Cherlin,Ehud Hrushovski
Publisher : Princeton University Press
Page : 204 pages
File Size : 43,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0691113319
Finite Structures with Few Types by Gregory L. Cherlin,Ehud Hrushovski Pdf
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, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.
Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics
Tian Ma,Shouhong Wang
Author : Tian Ma,Shouhong Wang
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 40,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836934
Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics by Tian Ma,Shouhong Wang Pdf
This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
An Introduction to Stability Theory
Anand Pillay
Author : Anand Pillay
Publisher : Courier Corporation
Page : 164 pages
File Size : 40,7 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9780486150437
An Introduction to Stability Theory by Anand Pillay Pdf
This introductory treatment covers the basic concepts and machinery of stability theory. Lemmas, corollaries, proofs, and notes assist readers in working through and understanding the material and applications. Full of examples, theorems, propositions, and problems, it is suitable for graduate students in logic and mathematics, professional mathematicians, and computer scientists. Chapter 1 introduces the notions of definable type, heir, and coheir. A discussion of stability and order follows, along with definitions of forking that follow the approach of Lascar and Poizat, plus a consideration of forking and the definability of types. Subsequent chapters examine superstability, dividing and ranks, the relation between types and sets of indiscernibles, and further properties of stable theories. The text concludes with proofs of the theorems of Morley and Baldwin-Lachlan and an extension of dimension theory that incorporates orthogonality of types in addition to regular types.
Stability Theorems in Geometry and Analysis
Yu.G. Reshetnyak
Author : Yu.G. Reshetnyak
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 40,5 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9789401583602
Stability Theorems in Geometry and Analysis by Yu.G. Reshetnyak Pdf
This is one of the first monographs to deal with the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isometric and other mappings. The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space, which is representative of a number of problems on stability for transformation classes. To enable this investigation a wide range of mathematical tools has been developed which incorporate the calculus of variation, estimates for differential operators like Korn inequalities, properties of functions with bounded mean oscillation, etc. Results obtained by others researching similar topics are mentioned, and a survey is given of publications treating relevant questions or involving the technique proposed. This volume will be of great value to graduate students and researchers interested in geometric function theory.