Groups And Model Theory
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| Author | : Olga Kharlampovich |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 244 |
| Release | : 2021-05-10 |
| Genre | : Mathematics |
| ISBN | : 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 .
| Author | : David M. Evans |
| Publisher | : Cambridge University Press |
| Total Pages | : 232 |
| Release | : 1997-07-10 |
| Genre | : Mathematics |
| ISBN | : 052158955X |
Surveys recent interactions between model theory and other branches of mathematics, notably group theory.
| Author | : Olga Kharlampovich |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 250 |
| Release | : 2021-05-10 |
| Genre | : Mathematics |
| ISBN | : 3110719762 |
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 .
| Author | : David Marker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 342 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387227342 |
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 | : Charles Loewner |
| Publisher | : Courier Corporation |
| Total Pages | : 128 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486462927 |
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.
| Author | : Lutz Strungmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 336 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 082186923X |
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.
| Author | : M Droste |
| Publisher | : CRC Press |
| Total Pages | : 516 |
| Release | : 1998-01-29 |
| Genre | : Mathematics |
| ISBN | : 9789056991012 |
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 | : Katrin Tent |
| Publisher | : Cambridge University Press |
| Total Pages | : 259 |
| Release | : 2012-03-08 |
| Genre | : Mathematics |
| ISBN | : 052176324X |
Concise introduction to current topics in model theory, including simple and stable theories.
| Author | : Anand Pillay |
| Publisher | : |
| Total Pages | : 209 |
| Release | : 1989 |
| Genre | : Group theory |
| ISBN | : 9780268013714 |
| Author | : Philipp Rothmaler |
| Publisher | : CRC Press |
| Total Pages | : 324 |
| Release | : 2018-12-07 |
| Genre | : Mathematics |
| ISBN | : 0429668503 |
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.
