Lectures on Infinitary Model Theory

Author: David Marker

Publisher: Cambridge University Press

ISBN: 1107181933

Category: Mathematics

Page: 192

View: 3815

Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
Posted in Mathematics

Model Theory and the Philosophy of Mathematical Practice

Formalization without Foundationalism

Author: John T. Baldwin

Publisher: Cambridge University Press

ISBN: 1108103014

Category: Science

Page: 352

View: 2902

Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.
Posted in Science

Model Theory : An Introduction

Author: David Marker

Publisher: Springer Science & Business Media

ISBN: 0387227342

Category: Mathematics

Page: 345

View: 2527

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
Posted in Mathematics

Lectures on Linear Logic

Author: Anne Sjerp Troelstra

Publisher: Center for the Study of Language and Information Publications

ISBN: 9780937073773

Category: Mathematics

Page: 215

View: 5856

The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
Posted in Mathematics

Use of Mathematical Literature

Author: Alison Rosemary Dorling

Publisher: Butterworth-Heinemann

ISBN: 9780408709132

Category: Reference

Page: 260

View: 7736

Posted in Reference

Logic Colloquium '02

Lecture Notes in Logic 27

Author: Zoé Chatzidakis,Peter Koepke,Wolfram Pohlers

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 359

View: 2108

This book is a compilation of papers presented at the 2002 European Summer Meeting of the Association for Symbolic Logic and the associated Colloquium Logicum 2002 conference. It includes tutorials and research articles from some of the world's preeminent logicians. Topics presented span all areas of mathematical logic, with a particular emphasis on Computability Theory and Proof Theory.
Posted in Mathematics

Lectures in Logic and Set Theory: Volume 2, Set Theory

Author: George Tourlakis

Publisher: Cambridge University Press

ISBN: 9780521753746

Category: Mathematics

Page: 592

View: 7949

Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).
Posted in Mathematics

Cambridge Summer School in Mathematical Logic

Held in Cambridge /U. K., August 1-21, 1971

Author: A. R. D. Mathias,H. Rogers

Publisher: Springer

ISBN: 9783540055693

Category: Mathematics

Page: 664

View: 4967

Posted in Mathematics

Subject Catalog

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 7159

Posted in

Model Theory

Author: Chen Chung Chang,H. Jerome Keisler

Publisher: North-Holland

ISBN: N.A

Category: Mathematics

Page: 554

View: 9185

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.
Posted in Mathematics

Logic Colloquium '77

Proceedings

Author: Angus Macintyre

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 311

View: 8710

Posted in Logic, Symbolic and mathematical

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Monographic series

Page: N.A

View: 2427

Posted in Monographic series

Mathematical Logic and Applications

Proceedings of the Logic Meeting held in Kyoto, 1987

Author: Juichi Shinoda,Theodore A. Slaman,Tosiyuki Tugue

Publisher: Springer

ISBN: 3540482202

Category: Mathematics

Page: 226

View: 5685

These proceedings include the papers presented at the logic meeting held at the Research Institute for Mathematical Sciences, Kyoto University, in the summer of 1987. The meeting mainly covered the current research in various areas of mathematical logic and its applications in Japan. Several lectures were also presented by logicians from other countries, who visited Japan in the summer of 1987.
Posted in Mathematics

Language in Action

Categories, Lambdas and Dynamic Logic

Author: Johan van Benthem

Publisher: MIT Press

ISBN: 9780262720243

Category: Language Arts & Disciplines

Page: 365

View: 9736

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.
Posted in Language Arts & Disciplines

A Guide to NIP Theories

Author: Pierre Simon

Publisher: Cambridge University Press

ISBN: 1107057752

Category: Mathematics

Page: 166

View: 6854

The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Posted in Mathematics