Model Theory And Algebraic Geometry
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Author | : Elisabeth Bouscaren |
Publisher | : Springer |
Total Pages | : 223 |
Release | : 2009-03-14 |
Genre | : Mathematics |
ISBN | : 3540685219 |
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 | : Elisabeth Bouscaren |
Publisher | : Springer Science & Business Media |
Total Pages | : 223 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 3540648631 |
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 | : 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 | : Elisabeth Bouscaren |
Publisher | : |
Total Pages | : 236 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662194478 |
Author | : Jörg Flum |
Publisher | : Springer |
Total Pages | : 161 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540385444 |
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 | : Lou van den Dries |
Publisher | : Springer |
Total Pages | : 201 |
Release | : 2014-09-20 |
Genre | : Mathematics |
ISBN | : 3642549365 |
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 | : Deirdre Haskell |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 2000-07-03 |
Genre | : Mathematics |
ISBN | : 9780521780681 |
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author | : Bradd T. Hart |
Publisher | : American Mathematical Soc. |
Total Pages | : 121 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827057 |
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 | : Sumio Watanabe |
Publisher | : Cambridge University Press |
Total Pages | : 295 |
Release | : 2009-08-13 |
Genre | : Computers |
ISBN | : 0521864674 |
Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.