Download or read book Model Theoretic Algebra With Particular Emphasis on Fields Rings Modules written by Christian.U Jensen and published by Routledge. This book was released on 2022-03-10 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.
Download or read book Model Theory Algebra and Geometry written by Deirdre Haskell and published by Cambridge University Press. This book was released on 2000-07-03 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 1998-01-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Download or read book Model Theory in Algebra Analysis and Arithmetic written by Lou van den Dries and published by Springer. This book was released on 2014-09-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Download or read book Mathematical Logic and Model Theory written by Alexander Prestel and published by Springer Science & Business Media. This book was released on 2011-08-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Download or read book Introduction to Model Theory written by Philipp Rothmaler and published by CRC Press. This book was released on 2018-12-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Download or read book Model Theory An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Download or read book Model Theory and Algebraic Geometry written by Elisabeth Bouscaren and published by Springer. This book was released on 2009-03-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Model Theoretic Algebra written by G. Cherlin and published by Springer. This book was released on 2006-11-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Model Theoretic Algebra written by G. Cherlin and published by . This book was released on 2014-01-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Shorter Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1997-04-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1993-03-11 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
Download or read book A Model Theoretic Oriented Approach to Partial Algebras written by P. Burmeister and published by Walter de Gruyter GmbH & Co KG. This book was released on 1986-12-31 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "A Model Theoretic Oriented Approach to Partial Algebras".
Download or read book Model Theory and Applications written by O.V. Belegradek and published by American Mathematical Soc.. This book was released on 1999 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.
Download or read book Model Theoretic Algebra written by Gregory L. Cherlin and published by Springer. This book was released on 1976 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Algebraic Model Theory written by Bradd T. Hart and published by American Mathematical Soc.. This book was released on 2002 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
