Groups And Model Theory
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Groups And Model Theory
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Author : Olga Kharlampovich
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-05-10
Groups And Model Theory written by Olga Kharlampovich and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-10 with Mathematics categories.
This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .
Groups Modules And Model Theory Surveys And Recent Developments
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Author : Manfred Droste
language : en
Publisher: Springer
Release Date : 2017-06-02
Groups Modules And Model Theory Surveys And Recent Developments written by Manfred Droste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-02 with Mathematics categories.
This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Model Theory Of Groups And Automorphism Groups
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Author : David M. Evans
language : en
Publisher: Cambridge University Press
Release Date : 1997-07-10
Model Theory Of Groups And Automorphism Groups written by David M. Evans and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-10 with Mathematics categories.
Surveys recent interactions between model theory and other branches of mathematics, notably group theory.
Model Theory And Applications
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Author : O.V. Belegradek
language : en
Publisher: American Mathematical Soc.
Release Date :
Model Theory And Applications written by O.V. Belegradek and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Introduction To Model Theory
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Author : Philipp Rothmaler
language : en
Publisher: CRC Press
Release Date : 2000-10-31
Introduction To Model Theory written by Philipp Rothmaler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-31 with Mathematics categories.
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.
Model Theory
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Author : C.C. Chang
language : en
Publisher: Courier Corporation
Release Date : 2013-10-03
Model Theory written by C.C. Chang and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.
This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
Model Theory Of Groups And Automorphism Groups
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Author : David Mark Evans
language : en
Publisher:
Release Date : 1997
Model Theory Of Groups And Automorphism Groups written by David Mark Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Group theory categories.
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.
Abelian Groups
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Author : Carol Jacoby
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-22
Abelian Groups written by Carol Jacoby and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abelian groups. A wide variety of ways to characterise different classes of abelian groups by invariants, isomorphisms and duality principles are discussed.
Model Theory
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Author : María Manzano
language : en
Publisher: Oxford University Press
Release Date : 1999
Model Theory written by María Manzano and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computers categories.
Model theory, which is concerned with the relationship between mathematical structures and logic, now has a wide range of applications in areas such as computing, philosophy, and linguistics. This book, suitable for both mathematicians and students from outside the field, provides a clear and readable introduction to the subject.
Lattice Ordered Groups
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Author : A.M. Glass
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Ordered Groups written by A.M. Glass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A lattice-ordered group is a mathematical structure combining a (partial) order (lattice) structure and a group structure (on a set) in a compatible way. Thus it is a composite structure, or, a set carrying two or more simple structures in a compatible way. The field of lattice-ordered groups turn up on a wide range of mathematical fields ranging from functional analysis to universal algebra. These papers address various aspects of the field, with wide applicability for interested researchers.