The Elements of Mathematical Logic

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Author: Paul C. Rosenbloom

Publisher: Courier Corporation

ISBN: 0486446174

Category: Mathematics

Page: 214

View: 4727

This introduction to mathematical logic stresses the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction to so-called undecidability and incompleteness theorems; and much more. 1950 edition.

The Elements of Advanced Mathematics

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Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 9780849384912

Category: Mathematics

Page: 176

View: 8572

Clearly written and easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material.

Direct and Converse Theorems

The Elements of Symbolic Logic

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Author: I. S. Gradshtein

Publisher: Elsevier

ISBN: 1483155072

Category: Mathematics

Page: 192

View: 2843

Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chapter explains several questions of mathematical logic–a science that is being developed in connection with the theory of mathematical proof. This edition is provided with a large number of problems and questions to help easily understand the material. The book is intended for students studying mathematics, specifically at intermediate colleges of various types. The text is also a useful reference for university students and teachers.

The Elements of Mathematical Semantics

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Author: Maurice V. Aldridge

Publisher: Walter de Gruyter

ISBN: 3110871432

Category: Language Arts & Disciplines

Page: 272

View: 5130

TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.

The Elements of Advanced Mathematics, Second Edition

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Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 9781584883036

Category: Mathematics

Page: 232

View: 5113

The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs. New in the Second Edition: Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor set Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection Streamlined treatment of non-Euclidean geometry Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations More thorough treatment of the Axiom of Choice and its equivalents Additional material on Russell's paradox and related ideas Expanded treatment of group theory that helps students grasp the axiomatic method A wealth of added exercises

Elements of Mathematical Logic

(Model Theory)

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Author: Georg Kreisel,Jean Louis Krivine

Publisher: Elsevier

ISBN: 9780444534125

Category: Electronic books

Page: 222

View: 6838

Elements of Intuitionism

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Author: Michael A. E. Dummett

Publisher: Oxford University Press

ISBN: 9780198505242

Category: Mathematics

Page: 331

View: 3469

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

A Concise Introduction to Mathematical Logic

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Author: Wolfgang Rautenberg

Publisher: Springer

ISBN: 9781441912213

Category: Mathematics

Page: 320

View: 3771

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.