Model Theory In Algebra Analysis And Arithmetic

Author : Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie
Publisher : Springer
Page : 201 pages
File Size : 53,9 Mb
Release : 2014-09-20
Category : Mathematics
ISBN : 9783642549366

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Model Theory in Algebra, Analysis and Arithmetic by Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie Pdf

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
Page : 342 pages
File Size : 51,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227344

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Model Theory : An Introduction by David Marker Pdf

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 : Deirdre Haskell,Anand Pillay,Charles Steinhorn
Publisher : Cambridge University Press
Page : 244 pages
File Size : 40,8 Mb
Release : 2000-07-03
Category : Mathematics
ISBN : 0521780683

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Model Theory, Algebra, and Geometry by Deirdre Haskell,Anand Pillay,Charles Steinhorn Pdf

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.

Author : Zoé Maria Chatzidakis
Publisher : Cambridge University Press
Page : 5 pages
File Size : 51,7 Mb
Release : 2008
Category : Algebra, Homological
ISBN : 9780521709088

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Model Theory with Applications to Algebra and Analysis by Zoé Maria Chatzidakis Pdf

The first of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and noncommutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this book will undoubtedly appeal to all mathematicians with an interest in model theory and its applications, from graduate students to senior researchers and from beginners to experts.

Author : Alexander Prestel,Charles N. Delzell
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 46,5 Mb
Release : 2011-08-21
Category : Mathematics
ISBN : 9781447121763

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Mathematical Logic and Model Theory by Alexander Prestel,Charles N. Delzell Pdf

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 : Bradd T. Hart,Matthew Valeriote
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 48,5 Mb
Release : 2002
Category : Algebraic fields
ISBN : 9780821827055

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Lectures on Algebraic Model Theory by Bradd T. Hart,Matthew Valeriote Pdf

This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.

Author : M Droste,R. Gobel
Publisher : CRC Press
Page : 512 pages
File Size : 45,9 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9781000717457

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Advances in Algebra and Model Theory by M Droste,R. Gobel Pdf

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 : Annalisa Marcja,Carlo Toffalori
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 48,7 Mb
Release : 2003
Category : Mathematics
ISBN : 1402013302

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A Guide to Classical and Modern Model Theory by Annalisa Marcja,Carlo Toffalori Pdf

Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world. This volume-is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.

Author : Chen Chung Chang,H. Jerome Keisler
Publisher : Courier Corporation
Page : 674 pages
File Size : 51,5 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486488219

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Model Theory by Chen Chung Chang,H. Jerome Keisler Pdf

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.

Author : Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 47,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589239

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Algebraic Model Theory by Bradd T. Hart,A. Lachlan,Matthew A. Valeriote Pdf

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 : Ieke Moerdijk,Jaap van Oosten
Publisher : Springer
Page : 141 pages
File Size : 44,8 Mb
Release : 2018-11-23
Category : Mathematics
ISBN : 9783319924144

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Sets, Models and Proofs by Ieke Moerdijk,Jaap van Oosten Pdf

This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

Author : Olga Kharlampovich,Rizos Sklinos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 244 pages
File Size : 43,7 Mb
Release : 2021-05-10
Category : Mathematics
ISBN : 9783110719710

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Groups and Model Theory by Olga Kharlampovich,Rizos Sklinos Pdf

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 : Zoé Maria Chatzidakis,School of Mathematical Sciences Dugald MacPherson,Professor of Mathematics Anand Pillay,Alex Wilkie
Publisher : Unknown
Page : 445 pages
File Size : 47,7 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107363004

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Model Theory with Applications to Algebra and Analysis by Zoé Maria Chatzidakis,School of Mathematical Sciences Dugald MacPherson,Professor of Mathematics Anand Pillay,Alex Wilkie Pdf

Account of current research in model theory and its connections with algebra and analysis; contributions from leaders in the field.

Author : W. A. J. Luxemburg
Publisher : Unknown
Page : 328 pages
File Size : 49,6 Mb
Release : 1969
Category : Mathematics
ISBN : STANFORD:36105031209815

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Applications of Model Theory to Algebra, Analysis, and Probability by W. A. J. Luxemburg Pdf

Author : Jose Iovino
Publisher : CRC Press
Page : 456 pages
File Size : 50,9 Mb
Release : 2017-08-14
Category : Mathematics
ISBN : 9781315351094

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Beyond First Order Model Theory, Volume I by Jose Iovino Pdf

Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.