Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

Model theory --- Logic, Symbolic and mathematical --- Model theory. --- Mathematical logic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume surveys recent interactions between model theory and other branches of mathematics, notably group theory. Beginning with an introductory chapter describing relevant background material, the book contains contributions from many leading international figures in this area. Topics described include automorphism groups of algebraically closed fields, the model theory of pseudo-finite fields and applications to the subgroup structure of finite Chevalley groups. Model theory of modules, and aspects of model theory of various classes of groups, including free groups, are also discussed. The book also contains the first comprehensive survey of finite covers. Many new proofs and simplifications of recent results are presented and the articles contain many open problems. This book will be a suitable guide for graduate students and a useful reference for researchers working in model theory and algebra.

Model theory --- Group theory --- Logic, Symbolic and mathematical --- Model theory. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Model theory - Congresses --- Group theory - Congresses

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Operator theory --- Operator theory. --- Opérateurs, Théorie des. --- Decomposition method. --- Décomposition (méthode mathématique) --- Model theory. --- Théorie des modèles. --- Decomposition method --- Model theory --- Functional analysis --- Logic, Symbolic and mathematical --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis --- Théorie des modèles

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Model theory --- Congresses --- Mathematical logic. --- Algebraic geometry. --- Functions of real variables. --- Group theory. --- Mathematical Logic and Foundations. --- Algebraic Geometry. --- Real Functions. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Real variables --- Functions of complex variables --- Algebraic geometry --- Geometry --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Model theory - Congresses

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im­ portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re­ cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap­ proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli­ cability of NSA more widely known and available to research mathemati­ cians.

Nonstandard mathematical analysis --- Congresses. --- Mathematical analysis [Nonstandard ] --- Congresses --- Mathematical analysis. --- Analysis (Mathematics). --- Probabilities. --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Fluids. --- Analysis. --- Probability Theory and Stochastic Processes. --- Functional Analysis. --- Applications of Mathematics. --- Fluid- and Aerodynamics. --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Engineering --- Engineering analysis --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.1 Mathematical analysis --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory --- Nonstandard mathematical analysis - Congresses