Constructibility
Constructibility

Author: Keith J. Devlin

Publisher: Cambridge University Press

Published: 2017-03-16

Total Pages: 438

ISBN-13: 110716835X

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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

Logic from A to Z
Logic from A to Z

Author: John B. Bacon

Publisher: Routledge

Published: 2013-09-05

Total Pages: 125

ISBN-13: 1134970978

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First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy. Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

The Axiom of Choice
The Axiom of Choice

Author: Thomas J. Jech

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 226

ISBN-13: 0486466248

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Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.

Almost Free Modules
Almost Free Modules

Author: P.C. Eklof

Publisher: Elsevier

Published: 2002-04-29

Total Pages: 620

ISBN-13: 0080527051

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This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

Philosophy of Mathematics
Philosophy of Mathematics

Author: Thomas Bedürftig

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-10-26

Total Pages: 476

ISBN-13: 3110468336

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The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection

Introduction to Set Theory, Revised and Expanded
Introduction to Set Theory, Revised and Expanded

Author: Karel Hrbacek

Publisher: CRC Press

Published: 2017-12-19

Total Pages: 310

ISBN-13: 1482276852

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Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.

Mathematical Logic
Mathematical Logic

Author: Joseph R. Shoenfield

Publisher: CRC Press

Published: 2018-05-02

Total Pages: 351

ISBN-13: 135143330X

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This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.