Download or read book Beyond First Order Model Theory Volume I written by Jose Iovino and published by CRC Press. This book was released on 2017-08-14 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Beyond First Order Model Theory Volume II written by Jose Iovino and published by CRC Press. This book was released on 2023-07-03 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Beyond First Order Model Theory written by José Iovino and published by . This book was released on 2017 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Beyond First Order Model Theory written by José Iovino and published by Chapman & Hall/CRC. This book was released on 2016-11-15 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Model Theory written by Philipp Rothmaler and published by CRC Press. This book was released on 2018-12-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Model Theory for Beginners 15 Lectures written by Roman Kossak and published by . This book was released on 2021-02-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
Download or read book Model Theory written by C.C. Chang and published by Elsevier. This book was released on 1990-06-12 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A First Course in Logic written by Shawn Hedman and published by OUP Oxford. This book was released on 2004-07-08 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
Download or read book A First Course in Linear Model Theory written by Nalini Ravishanker and published by CRC Press. This book was released on 2001-12-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Model Theory of Operator Algebras written by Isaac Goldbring and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extensions of First Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.
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.
Download or read book Model Theory An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Finite Model Theory written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.
Download or read book A Guide to Classical and Modern Model Theory written by Annalisa Marcja and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
