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Author : Angus Macintyre
Publisher : Unknown
Page : 218 pages
File Size : 49,5 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015056471173
Author : Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 42,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589239
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 : Deirdre Haskell,Anand Pillay,Charles Steinhorn
Publisher : Cambridge University Press
Page : 244 pages
File Size : 41,9 Mb
Release : 2000-07-03
Category : Mathematics
ISBN : 0521780683
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author : David Marker,Margit Messmer,Anand Pillay
Publisher : Cambridge University Press
Page : 165 pages
File Size : 50,8 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168077
This book introduces the active area of the model theory of fields, concentrating on connections to stability theory.
Author : Zoé Maria Chatzidakis
Publisher : Cambridge University Press
Page : 5 pages
File Size : 43,5 Mb
Release : 2008
Category : Algebra, Homological
ISBN : 9780521709088
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 : Zoé Chatzidakis
Publisher : Unknown
Page : 128 pages
File Size : 54,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : OCLC:894590425
Author : Elisabeth Bouscaren
Publisher : Springer
Page : 223 pages
File Size : 54,9 Mb
Release : 2009-03-14
Category : Mathematics
ISBN : 9783540685210
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 : Phillip A. Griffiths,John Frank Adams
Publisher : Princeton University Press
Page : 228 pages
File Size : 55,8 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400869268
This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories. Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pn 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pn; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to Pn; 5.2 Grassmanians and vector bundles; 5.3 Chern classes and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology theory; 7.1 the Chern character and obstruction theory; 7.2 the Atiyah-Hirzebruch spectral sequence; 7.3 K-theory on algebraic varieties; 8.1 Stein manifold theory; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding remarks; bibliography. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Nigel J. Cutland,Mauro Di Nasso,David A. Ross
Publisher : Cambridge University Press
Page : 248 pages
File Size : 45,5 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108621298
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 twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.
Author : Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie
Publisher : Springer
Page : 201 pages
File Size : 45,9 Mb
Release : 2014-09-20
Category : Mathematics
ISBN : 9783642549366
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 : 54,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227344
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 : Hans Schoutens
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 45,7 Mb
Release : 2010-07-31
Category : Mathematics
ISBN : 9783642133671
Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
Author : Vladimir G. Berkovich
Publisher : American Mathematical Soc.
Page : 181 pages
File Size : 44,7 Mb
Release : 2012-08-02
Category : Mathematics
ISBN : 9780821890202
The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.
Author : Bradd T. Hart
Publisher : American Mathematical Soc.
Page : 440 pages
File Size : 53,8 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 9780821883822
Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.
Author : Tim Button,Sean P. Walsh
Publisher : Oxford University Press
Page : 534 pages
File Size : 55,5 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198790396
Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.