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Author: Deirdre Haskell
Publisher: Cambridge University Press
Published: 2000-07-03
Total Pages: 244
ISBN-13: 9780521780681
DOWNLOAD EBOOK →Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author: Elisabeth Bouscaren
Publisher: Springer
Published: 2009-03-14
Total Pages: 223
ISBN-13: 3540685219
DOWNLOAD EBOOK →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.
Author: Lou van den Dries
Publisher: Springer
Published: 2014-09-20
Total Pages: 201
ISBN-13: 3642549365
DOWNLOAD EBOOK →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.
Author: David Marker
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 342
ISBN-13: 0387227342
DOWNLOAD EBOOK →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
Author: Katrin Tent
Publisher: Cambridge University Press
Published: 2012-03-08
Total Pages: 259
ISBN-13: 052176324X
DOWNLOAD EBOOK →Concise introduction to current topics in model theory, including simple and stable theories.
Author: M Droste
Publisher: CRC Press
Published: 2019-08-16
Total Pages: 516
ISBN-13: 1000725278
DOWNLOAD EBOOK →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.
Author: Sumio Watanabe
Publisher: Cambridge University Press
Published: 2009-08-13
Total Pages: 295
ISBN-13: 0521864674
DOWNLOAD EBOOK →Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
Author: Bradd T. Hart
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 285
ISBN-13: 9401589232
DOWNLOAD EBOOK →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.
Author: Alexander Prestel
Publisher: Springer Science & Business Media
Published: 2011-08-21
Total Pages: 198
ISBN-13: 1447121767
DOWNLOAD EBOOK →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.
Author: Wilfrid Hodges
Publisher: Cambridge University Press
Published: 1993-03-11
Total Pages: 810
ISBN-13: 9780521304429
DOWNLOAD EBOOK →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.
