[PDF] Model Theory And Algebraic Geometry eBook

Author : Elisabeth Bouscaren
Publisher : Springer
Page : 223 pages
File Size : 45,91 MB
Release : 2009-03-14
Category : Mathematics
ISBN : 3540685219

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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
Page : 223 pages
File Size : 33,58 MB
Release : 1998
Category : Mathematics
ISBN : 3540648631

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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 : Lou van den Dries
Publisher : Springer
Page : 201 pages
File Size : 42,95 MB
Release : 2014-09-20
Category : Mathematics
ISBN : 3642549365

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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 : 49,27 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387227342

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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 : M Droste
Publisher : CRC Press
Page : 516 pages
File Size : 17,47 MB
Release : 1998-01-29
Category : Mathematics
ISBN : 9789056991012

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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 : Mohamed Elkadi
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 23,75 MB
Release : 2006-11-02
Category : Mathematics
ISBN : 3540332758

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This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.

Author : Deirdre Haskell
Publisher : Cambridge University Press
Page : 244 pages
File Size : 39,42 MB
Release : 2000-07-03
Category : Mathematics
ISBN : 9780521780681

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

Author : Sumio Watanabe
Publisher : Cambridge University Press
Page : 295 pages
File Size : 18,8 MB
Release : 2009-08-13
Category : Computers
ISBN : 0521864674

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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.