Algebraic Model Theory

Author : Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 48,5 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 : Bradd T. Hart,Matthew Valeriote
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 51,9 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 : 516 pages
File Size : 50,9 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9781000725278

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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 : Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie
Publisher : Springer
Page : 195 pages
File Size : 47,5 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 : Elisabeth Bouscaren
Publisher : Springer
Page : 223 pages
File Size : 48,8 Mb
Release : 2009-03-14
Category : Mathematics
ISBN : 9783540685210

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Model Theory and Algebraic Geometry by Elisabeth Bouscaren Pdf

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.

Author : Deirdre Haskell,Anand Pillay,Charles Steinhorn
Publisher : Cambridge University Press
Page : 244 pages
File Size : 44,9 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 : David Marker
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 41,8 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 : Alexander Prestel,Charles N. Delzell
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 47,6 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 : Annalisa Marcja,Carlo Toffalori
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 53,7 Mb
Release : 2012-09-10
Category : Philosophy
ISBN : 9789400708129

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

This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.

Author : Philipp Rothmaler
Publisher : CRC Press
Page : 324 pages
File Size : 44,6 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429668500

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Introduction to Model Theory by Philipp Rothmaler Pdf

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.

Author : Angus Macintyre
Publisher : Unknown
Page : 218 pages
File Size : 43,9 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015056471173

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Connections Between Model Theory and Algebraic and Analytic Geometry by Angus Macintyre Pdf

Author : David Marker,Margit Messmer,Anand Pillay
Publisher : Cambridge University Press
Page : 165 pages
File Size : 40,8 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168077

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Model Theory of Fields by David Marker,Margit Messmer,Anand Pillay Pdf

This book introduces the active area of the model theory of fields, concentrating on connections to stability theory.

Author : Cyrus F. Nourani
Publisher : CRC Press
Page : 302 pages
File Size : 49,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781482231502

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A Functorial Model Theory by Cyrus F. Nourani Pdf

This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.

Author : Haimanti Sarbadhikari,Shashi Mohan Srivastava
Publisher : Springer
Page : 291 pages
File Size : 52,9 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9789811050985

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A Course on Basic Model Theory by Haimanti Sarbadhikari,Shashi Mohan Srivastava Pdf

This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.

Author : E.G. Manes
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461298601

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Algebraic Theories by E.G. Manes Pdf

In the past decade, category theory has widened its scope and now inter acts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chap ter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathe maticians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book.