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Groups and Model Theory

Author: Olga Kharlampovich

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-05-10

Total Pages: 244

ISBN-13: 3110719711

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 of Groups and Automorphism Groups

Author: David M. Evans

Publisher: Cambridge University Press

Published: 1997-07-10

Total Pages: 232

ISBN-13: 052158955X

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Surveys recent interactions between model theory and other branches of mathematics, notably group theory.

Groups and Model Theory

Author: Olga Kharlampovich

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-05-10

Total Pages: 250

ISBN-13: 3110719762

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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

Author: David Marker

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 342

ISBN-13: 0387227342

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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

Theory of Continuous Groups

Author: Charles Loewner

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 128

ISBN-13: 0486462927

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Based on lectures by a renowned educator, this book focuses on continuous groups, particularly in terms of applications in geometry and analysis. The author's unique perspectives are illustrated by numerous inventive geometric examples, many of which were inspired by footnotes among the work of Sophus Lie. 1971 edition.

Groups and Model Theory

Author: Lutz Strungmann

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 336

ISBN-13: 082186923X

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Contains the proceedings of the conference Groups and Model Theory, held 2011, in Ruhr, Germany. Articles cover abelian groups, modules over commutative rings, permutation groups, automorphism groups of homogeneous structures such as graphs, relational structures, geometries, topological spaces or groups, consequences of model theoretic properties like stability or categoricity, subgroups of small index, the automorphism tower problem, as well as random constructions.

Advances in Algebra and Model Theory

Author: M Droste

Publisher: CRC Press

Published: 1998-01-29

Total Pages: 516

ISBN-13: 9789056991012

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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.