Lectures In Model Theory

Author : Bradd T. Hart,Matthew Valeriote
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 55,9 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 : Franziska Jahnke,Daniel Palacín,Katrin Tent
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 2018
Category : Electronic
ISBN : 303719684X

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Lectures in Model Theory by Franziska Jahnke,Daniel Palacín,Katrin Tent Pdf

Author : Katrin Tent,Martin Ziegler
Publisher : Cambridge University Press
Page : 259 pages
File Size : 55,8 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780521763240

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A Course in Model Theory by Katrin Tent,Martin Ziegler Pdf

Concise introduction to current topics in model theory, including simple and stable theories.

Author : Franziska Jahnke,Daniel Palacín,Katrin Tent
Publisher : Unknown
Page : 128 pages
File Size : 51,6 Mb
Release : 2018
Category : Electronic
ISBN : 3037191848

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Lectures in Model Theory by Franziska Jahnke,Daniel Palacín,Katrin Tent Pdf

Author : David Marker
Publisher : Cambridge University Press
Page : 192 pages
File Size : 52,5 Mb
Release : 2016-10-27
Category : Mathematics
ISBN : 9781107181939

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Lectures on Infinitary Model Theory by David Marker Pdf

This book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic, and applications to algebra and algebraic geometry are both comprehensively explored.

Author : Roman Kossak
Publisher : Unknown
Page : 152 pages
File Size : 50,9 Mb
Release : 2021-02-10
Category : Electronic
ISBN : 1848903618

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Model Theory for Beginners. 15 Lectures by Roman Kossak Pdf

This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.

Author : David Marker,Margit Messmer,Anand Pillay
Publisher : Cambridge University Press
Page : 165 pages
File Size : 41,6 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 : Roman Kossak
Publisher : Unknown
Page : 152 pages
File Size : 49,8 Mb
Release : 2021-02-10
Category : Electronic
ISBN : 1848903618

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Model Theory for Beginners. 15 Lectures by Roman Kossak Pdf

This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.

Author : Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 41,8 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 : Jonathan Kirby
Publisher : Cambridge University Press
Page : 197 pages
File Size : 50,6 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781107163881

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An Invitation to Model Theory by Jonathan Kirby Pdf

An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

Author : Katrin Tent,Martin Ziegler
Publisher : Unknown
Page : 248 pages
File Size : 44,9 Mb
Release : 2012
Category : Model theory
ISBN : 1107224756

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A Course in Model Theory: Simple Theories by Katrin Tent,Martin Ziegler Pdf

This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

Author : Wilfrid Hodges
Publisher : Cambridge University Press
Page : 322 pages
File Size : 50,9 Mb
Release : 1997-04-10
Category : Mathematics
ISBN : 0521587131

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A Shorter Model Theory by Wilfrid Hodges Pdf

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 53,6 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

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Lectures on Invariant Theory by Igor Dolgachev Pdf

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Author : Gerald E. Sacks
Publisher : World Scientific Publishing Company
Page : 228 pages
File Size : 49,6 Mb
Release : 2010
Category : Mathematics
ISBN : UCSD:31822037486628

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Saturated Model Theory by Gerald E. Sacks Pdf

This book contains the material for a first course in pure model theory with applications to differentially closed fields. Topics covered in this book include saturated model criteria for model completeness and elimination of quantifiers; Morley rank and degree of element types; categoricity in power; two-cardinal theorems; existence and uniqueness of prime model extensions of substructures of models of totally transcendental theories; and homogeneity of models of ϖ1-categorical theories.

Author : Sergio Fajardo,H. Jerome Keisler
Publisher : A K Peters/CRC Press
Page : 140 pages
File Size : 48,7 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 1568811721

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Model Theory of Stochastic Processes by Sergio Fajardo,H. Jerome Keisler Pdf

This book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them.