Classification Of Countable Models Of Complete Theories Art 2

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Generalized Descriptive Set Theory And Classification Theory

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Author : Sy-David Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-05

Generalized Descriptive Set Theory And Classification Theory written by Sy-David Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Algebraic Model Theory

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Author : Bradd T. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Algebraic Model Theory written by Bradd T. Hart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

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.

Classification Theory

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Author : S. Shelah
language : en
Publisher: Elsevier
Release Date : 1990-12-06

Classification Theory written by S. Shelah and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-06 with Computers categories.

In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text.The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m

Model Theory And Modules

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Author : Mike Prest
language : en
Publisher: Cambridge University Press
Release Date : 1988-02-25

Model Theory And Modules written by Mike Prest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-02-25 with Mathematics categories.

In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.

Logic Colloquium 03

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Author : Viggo Stoltenberg-Hansen
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30

Logic Colloquium 03 written by Viggo Stoltenberg-Hansen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Mathematics categories.

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-fourth publication in the Lecture Notes in Logic series, contains the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland, in August 2003. These articles include an extended tutorial on generalizing finite model theory, as well as seventeen original research articles spanning all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.

A Guide To Classical And Modern Model Theory

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Author : Annalisa Marcja
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-30

A Guide To Classical And Modern Model Theory written by Annalisa Marcja and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Mathematics categories.

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.

Model Theory And Applications

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Author : O.V. Belegradek
language : en
Publisher: American Mathematical Soc.
Release Date :

Model Theory And Applications written by O.V. Belegradek and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.

Introduction To Model Theory

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Author : Philipp Rothmaler
language : en
Publisher: CRC Press
Release Date : 2018-12-07

Introduction To Model Theory written by Philipp Rothmaler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.

Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.

Groups Modules And Model Theory Surveys And Recent Developments

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Author : Manfred Droste
language : en
Publisher: Springer
Release Date : 2017-06-02

Groups Modules And Model Theory Surveys And Recent Developments written by Manfred Droste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-02 with Mathematics categories.

This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Classification Theory

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Author : John T. Baldwin
language : en
Publisher: Springer
Release Date : 2006-11-14

Classification Theory written by John T. Baldwin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.