Beyond First Order Model Theory Volume I
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Author | : Jose Iovino |
Publisher | : CRC Press |
Total Pages | : 427 |
Release | : 2017-08-14 |
Genre | : Mathematics |
ISBN | : 1498754015 |
Download Beyond First Order Model Theory, Volume I Book in PDF, Epub and Kindle
Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.
Author | : Jose Iovino |
Publisher | : CRC Press |
Total Pages | : 327 |
Release | : 2023-07-03 |
Genre | : Mathematics |
ISBN | : 0429554192 |
Download Beyond First Order Model Theory, Volume II Book in PDF, Epub and Kindle
A coherent introduction to current trends in model theory Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together Suitable as a reference for advanced undergraduate, postgraduates, and researchers Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature The various chapters in the book can be studied independently.
Author | : José Iovino |
Publisher | : |
Total Pages | : 427 |
Release | : 2017 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : 9781315332055 |
Download Beyond First Order Model Theory Book in PDF, Epub and Kindle
Author | : José Iovino |
Publisher | : Chapman & Hall/CRC |
Total Pages | : 427 |
Release | : 2016-11-15 |
Genre | : Mathematics |
ISBN | : 9781315368078 |
Download Beyond First Order Model Theory Book in PDF, Epub and Kindle
The traditional logical language of model theory is first-order logic. This language was proposed in the late 19th by G. Frege, and throughout the 20th century, it remained at the center of the development of model theory. Model theory is one of the central branches of mathematical logic and the field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students (graduate and advanced undergraduate) and senior researchers alike.
Author | : Wilfrid Hodges |
Publisher | : Cambridge University Press |
Total Pages | : 322 |
Release | : 1997-04-10 |
Genre | : Mathematics |
ISBN | : 9780521587136 |
Download A Shorter Model Theory Book in PDF, Epub and Kindle
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 | : Philipp Rothmaler |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2018-12-07 |
Genre | : Mathematics |
ISBN | : 0429668503 |
Download Introduction to Model Theory Book in PDF, Epub and Kindle
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.
Author | : Roman Kossak |
Publisher | : |
Total Pages | : 152 |
Release | : 2021-02-10 |
Genre | : |
ISBN | : 9781848903616 |
Download Model Theory for Beginners. 15 Lectures Book in PDF, Epub and Kindle
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 | : C.C. Chang |
Publisher | : Elsevier |
Total Pages | : 667 |
Release | : 1990-06-12 |
Genre | : Computers |
ISBN | : 008088007X |
Download Model Theory Book in PDF, Epub and Kindle
Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
Author | : Nalini Ravishanker |
Publisher | : CRC Press |
Total Pages | : 494 |
Release | : 2001-12-21 |
Genre | : Mathematics |
ISBN | : 9781584882473 |
Download A First Course in Linear Model Theory Book in PDF, Epub and Kindle
This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Author | : Isaac Goldbring |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 498 |
Release | : 2023-07-24 |
Genre | : Mathematics |
ISBN | : 3110768283 |
Download Model Theory of Operator Algebras Book in PDF, Epub and Kindle
Continuous model theory is an extension of classical first order logic which is best suited for classes of structures which are endowed with a metric. Applications have grown considerably in the past decade. This book is dedicated to showing how the techniques of continuous model theory are used to study C*-algebras and von Neumann algebras. This book geared to researchers in both logic and functional analysis provides the first self-contained collection of articles surveying the many applications of continuous logic to operator algebras that have been obtained in the last 15 years.