Mathematics

Model Theory, Algebra, and Geometry

Author: Deirdre Haskell,Anand Pillay,Charles Steinhorn

Publisher: Cambridge University Press

ISBN: 9780521780681

Category: Mathematics

Page: 227

View: 1157

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

Model Theory and Algebraic Geometry

An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture

Author: Elisabeth Bouscaren

Publisher: Springer

ISBN: 3540685219

Category: Mathematics

Page: 216

View: 4682

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.
Philosophy

A Guide to Classical and Modern Model Theory

Author: Annalisa Marcja,Carlo Toffalori

Publisher: Springer Science & Business Media

ISBN: 9400708122

Category: Philosophy

Page: 371

View: 1834

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.
Mathematics

Model Theory in Algebra, Analysis and Arithmetic

Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori

Author: Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie

Publisher: Springer

ISBN: 3642549365

Category: Mathematics

Page: 195

View: 5983

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.
Mathematics

Algebraic Model Theory

Author: Bradd T. Hart,A. Lachlan,Matthew A. Valeriote

Publisher: Springer Science & Business Media

ISBN: 9401589232

Category: Mathematics

Page: 277

View: 8538

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.
Mathematics

Algebra, Logic and Combinatorics

Author: Shaun Bullett,Tom Fearn,Frank Smith

Publisher: World Scientific

ISBN: 1786340321

Category: Mathematics

Page: 184

View: 8712

This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics. Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas. Contents:Enumerative Combinatorics (Peter J Cameron)Introduction to the Finite Simple Groups (Robert A Wilson)Introduction to Representations of Algebras and Quivers (Anton Cox)The Invariant Theory of Finite Groups (Peter Fleischmann and James Shank)Model Theory (Ivan Tomašić) Readership: Researchers, graduate or PhD mathematical-science students who require a reference book that covers algebra, logic or combinatorics.
Mathematics

Logic Colloquium 2000

Author: René Cori,Alexander Razborov,Stevo Todorčević,Carol Wood

Publisher: Cambridge University Press

ISBN: 1108756034

Category: Mathematics

Page: N.A

View: 6847

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic.
Mathematics

Model Theory : An Introduction

Author: David Marker

Publisher: Springer Science & Business Media

ISBN: 0387227342

Category: Mathematics

Page: 345

View: 7554

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
Mathematics

Model Theory and the Philosophy of Mathematical Practice

Author: John Baldwin,John T. Baldwin

Publisher: Cambridge University Press

ISBN: 1107189217

Category: Mathematics

Page: 384

View: 7894

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Mathematics

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry:

Author: Raf Cluckers,Johannes Nicaise,Julien Sebag

Publisher: Cambridge University Press

ISBN: 1139499793

Category: Mathematics

Page: N.A

View: 8792

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces.
Mathematics

Alfred Tarski

Early Work in Poland—Geometry and Teaching

Author: Andrew McFarland,Joanna McFarland,James T. Smith

Publisher: Springer

ISBN: 149391474X

Category: Mathematics

Page: 499

View: 4416

Alfred Tarski (1901–1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now. This self-contained book focuses on Tarski’s early contributions to geometry and mathematics education, including the famous Banach–Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski’s later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski’s years in Poland. Alfred Tarski: Early Work in Poland serves the mathematical, educational, philosophical and historical communities by publishing Tarski’s early writings in a broadly accessible form, providing background from archival work in Poland and updating Tarski’s bibliography.
Mathematics

Algebraic Geometry Modeling in Information Theory

Author: Edgar Martínez-Moro

Publisher: World Scientific

ISBN: 9814335754

Category: Mathematics

Page: 325

View: 3740

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
Mathematics

Hilbert's Tenth Problem

Relations with Arithmetic and Algebraic Geometry : Workshop on Hilbert's Tenth Problem : Relations with Arithmetic and Algebraic Geometry, November 2-5, 1999, Ghent University, Belgium

Author: Ernst Dieterichs

Publisher: American Mathematical Soc.

ISBN: 0821826220

Category: Mathematics

Page: 367

View: 1205

This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bucchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation.The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory.
Mathematics

Differential Algebra and Related Topics

Proceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000

Author: Li Guo

Publisher: World Scientific

ISBN: 9789810247034

Category: Mathematics

Page: 305

View: 2000

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.
Mathematics

Trends in Commutative Algebra

Author: Luchezar L. Avramov

Publisher: Cambridge University Press

ISBN: 0521831954

Category: Mathematics

Page: 254

View: 2025

In 2002, an introductory workshop was held at the Mathematical Sciences Research Institute in Berkeley to survey some of the many directions of the commutative algebra field. Six principal speakers each gave three lectures, accompanied by a help session, describing the interaction of commutative algebra with other areas of mathematics for a broad audience of graduate students and researchers. This book is based on those lectures, together with papers from contributing researchers. David Benson and Srikanth Iyengar present an introduction to the uses and concepts of commutative algebra in the cohomology of groups. Mark Haiman considers the commutative algebra of n points in the plane. Ezra Miller presents an introduction to the Hilbert scheme of points to complement Professor Haiman's paper. Further contributors include David Eisenbud and Jessica Sidman; Melvin Hochster; Graham Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and Ana Bravo.
Mathematics

Stable Groups

Author: Frank Olaf Wagner

Publisher: Cambridge University Press

ISBN: 9780521598392

Category: Mathematics

Page: 309

View: 1195

In this book the general theory of stable groups is developed from the beginning.