Groups and Model Theory

Groups and Model Theory PDF

Author: Olga Kharlampovich

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-05-10

Total Pages: 250

ISBN-13: 3110719762

DOWNLOAD EBOOK →

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 .

Model Theory : An Introduction

Model Theory : An Introduction PDF

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

Advances in Algebra and Model Theory

Advances in Algebra and Model Theory PDF

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.

Groups, Modules, and Model Theory - Surveys and Recent Developments

Groups, Modules, and Model Theory - Surveys and Recent Developments PDF

Author: Manfred Droste

Publisher: Springer

Published: 2017-06-02

Total Pages: 475

ISBN-13: 331951718X

DOWNLOAD EBOOK →

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.

A Shorter Model Theory

A Shorter Model Theory PDF

Author: Wilfrid Hodges

Publisher: Cambridge University Press

Published: 1997-04-10

Total Pages: 322

ISBN-13: 9780521587136

DOWNLOAD EBOOK →

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.

Group Theory for the Standard Model of Particle Physics and Beyond

Group Theory for the Standard Model of Particle Physics and Beyond PDF

Author: Ken J. Barnes

Publisher: CRC Press

Published: 2010-03-10

Total Pages: 0

ISBN-13: 9781420078749

DOWNLOAD EBOOK →

Based on the author’s well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries. After linking symmetries with conservation laws, the book works through the mathematics of angular momentum and extends operators and functions of classical mechanics to quantum mechanics. It then covers the mathematical framework for special relativity and the internal symmetries of the standard model of elementary particle physics. In the chapter on Noether’s theorem, the author explains how Lagrangian formalism provides a natural framework for the quantum mechanical interpretation of symmetry principles. He then examines electromagnetic, weak, and strong interactions; spontaneous symmetry breaking; the elusive Higgs boson; and supersymmetry. He also introduces new techniques based on extending space–time into dimensions described by anticommuting coordinates. Designed for graduate and advanced undergraduate students in physics, this text provides succinct yet complete coverage of the group theory of the symmetries of the standard model of elementary particle physics. It will help students understand current knowledge about the standard model as well as the physics that potentially lies beyond the standard model.

Geometric Stability Theory

Geometric Stability Theory PDF

Author: Anand Pillay

Publisher: Oxford University Press on Demand

Published: 1996

Total Pages: 361

ISBN-13: 9780198534372

DOWNLOAD EBOOK →

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.

Lanterna Rally - Theme by Grace Themes