Models And Ultraproducts

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Models and Ultraproducts

Author : John Lane Bell
Publisher : Courier Corporation
ISBN 13 : 0486449793
Total Pages : 338 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Models and Ultraproducts by : John Lane Bell

Download or read book Models and Ultraproducts written by John Lane Bell and published by Courier Corporation. This book was released on 2006-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

Models and Ultraproducts

Author : A. B. Slomson
Publisher : Dover Publications
ISBN 13 : 9780486788630
Total Pages : 336 pages
Book Rating : 4.7/5 (886 download)

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Book Synopsis Models and Ultraproducts by : A. B. Slomson

Download or read book Models and Ultraproducts written by A. B. Slomson and published by Dover Publications. This book was released on 2013-12-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition.

Models and Ultraproducts

Author : John Lane Bell
Publisher :
ISBN 13 :
Total Pages : 322 pages
Book Rating : 4.:/5 (977 download)

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Book Synopsis Models and Ultraproducts by : John Lane Bell

Download or read book Models and Ultraproducts written by John Lane Bell and published by . This book was released on 1971 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Models and Ultraproducts

Author : John Lane Bell
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis Models and Ultraproducts by : John Lane Bell

Download or read book Models and Ultraproducts written by John Lane Bell and published by . This book was released on 1971 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an elementary exposition of some of the basic concepts of model theory. Model theory, which can be described briefly as the study of the relationship between formal languages and abstract structures, covers a very wide field and it is not possible to compress it into one volume. We have chosen as our theme the ultraproducts construction. We hope this book we be of use to undergraduate and practicing mathematicians.

Model Theory

Author :
Publisher :
ISBN 13 : 9780720422009
Total Pages : 0 pages
Book Rating : 4.4/5 (22 download)

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Book Synopsis Model Theory by :

Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continuous Model Theory. (AM-58), Volume 58

Author : Chen Chung Chang
Publisher : Princeton University Press
ISBN 13 : 1400882052
Total Pages : 165 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Continuous Model Theory. (AM-58), Volume 58 by : Chen Chung Chang

Download or read book Continuous Model Theory. (AM-58), Volume 58 written by Chen Chung Chang and published by Princeton University Press. This book was released on 2016-03-02 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a study of the theory of models with truth values in a compact Hausdorff topological space.

A Shorter Model Theory

Author : Wilfrid Hodges
Publisher : Cambridge University Press
ISBN 13 : 9780521587136
Total Pages : 322 pages
Book Rating : 4.5/5 (871 download)

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Book Synopsis A Shorter Model Theory by : Wilfrid Hodges

Download or read book A Shorter Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1997-04-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Institution-independent Model Theory

Author : Razvan Diaconescu
Publisher : Springer Science & Business Media
ISBN 13 : 3764387084
Total Pages : 377 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Institution-independent Model Theory by : Razvan Diaconescu

Download or read book Institution-independent Model Theory written by Razvan Diaconescu and published by Springer Science & Business Media. This book was released on 2008-08-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called ‘institution theory’. The development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a rather large diverse collection of logics from the mathematical and computer science practice.

Ultraproducts in the Theory of Models

Author : Simon Bernard Kochen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (142 download)

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Book Synopsis Ultraproducts in the Theory of Models by : Simon Bernard Kochen

Download or read book Ultraproducts in the Theory of Models written by Simon Bernard Kochen and published by . This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Primer of Infinitesimal Analysis

Author : John L. Bell
Publisher : Cambridge University Press
ISBN 13 : 0521887186
Total Pages : 7 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis A Primer of Infinitesimal Analysis by : John L. Bell

Download or read book A Primer of Infinitesimal Analysis written by John L. Bell and published by Cambridge University Press. This book was released on 2008-04-07 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Toposes and Local Set Theories

Author : John L. Bell
Publisher : Courier Corporation
ISBN 13 : 0486462862
Total Pages : 290 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Toposes and Local Set Theories by : John L. Bell

Download or read book Toposes and Local Set Theories written by John L. Bell and published by Courier Corporation. This book was released on 2008-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Logic of Mathematics

Author : Zofia Adamowicz
Publisher : John Wiley & Sons
ISBN 13 : 1118030796
Total Pages : 276 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Logic of Mathematics by : Zofia Adamowicz

Download or read book Logic of Mathematics written by Zofia Adamowicz and published by John Wiley & Sons. This book was released on 2011-09-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Hilbert's Fifth Problem and Related Topics

Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 147041564X
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hilbert's Fifth Problem and Related Topics by : Terence Tao

Download or read book Hilbert's Fifth Problem and Related Topics written by Terence Tao and published by American Mathematical Soc.. This book was released on 2014-07-18 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.

The Theory of Ultrafilters

Author : W.W. Comfort
Publisher : Springer Science & Business Media
ISBN 13 : 364265780X
Total Pages : 494 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis The Theory of Ultrafilters by : W.W. Comfort

Download or read book The Theory of Ultrafilters written by W.W. Comfort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e. , to the Stone-Cech com pactification process (implying the Tychonoff theorem on the compact ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work.

Classification Theory

Author : S. Shelah
Publisher : Elsevier
ISBN 13 : 9780080880242
Total Pages : 740 pages
Book Rating : 4.8/5 (82 download)

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Book Synopsis Classification Theory by : S. Shelah

Download or read book Classification Theory written by S. Shelah and published by Elsevier. This book was released on 1990-12-06 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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|M|. This theorem is also the subject of Chapter XIII.

A Course in Model Theory

Author : Katrin Tent
Publisher : Cambridge University Press
ISBN 13 : 052176324X
Total Pages : 259 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis A Course in Model Theory by : Katrin Tent

Download or read book A Course in Model Theory written by Katrin Tent and published by Cambridge University Press. This book was released on 2012-03-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to current topics in model theory, including simple and stable theories.

A Functorial Model Theory

Author : Cyrus F. Nourani
Publisher : CRC Press
ISBN 13 : 1482231506
Total Pages : 302 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Functorial Model Theory by : Cyrus F. Nourani

Download or read book A Functorial Model Theory written by Cyrus F. Nourani and published by CRC Press. This book was released on 2016-04-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.