An Introduction to Metalogic

An Introduction to Metalogic

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Description

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic, and ends with detailed outlines of the proofs of the incompleteness, undecidability and indefinability theorems. Many other topics are covered: expressive completeness, the basics of set theory, infinite cardinalities, Cantor's Theorems, the Soundness and Completeness Theorems, Turing machines, the Halting Problem, predicate logic theories and their properties, elementary equivalence, isomorphism, Peano Arithmetic, second-order predicate logic and more.

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Product details

  • Paperback | 300 pages
  • 178 x 226 x 18mm | 599.99g
  • Broadview Press Ltd
  • Peterborough, Canada
  • English
  • 1554811716
  • 9781554811717
  • 979,164

Review quote

“This is an excellent text in intermediate logic that should be warmly received by students. The well-paced exposition is remarkably clear. The choice of material, including remarks on the philosophical significance of the principal theorems and welcome sections on Second-Order logic, seems just right. And the ample exercises at the end of each chapter, which range from easy to difficult, not only test the reader’s understanding, but move the subject forward. Highly recommended.” — David Keyt, Research Professor, University of Arizona; Professor Emeritus, University of Washington “An Introduction to Metalogic provides extensive coverage of the usual meta-theoretic results concerning the standard logical systems. It covers the completeness theorems, compactness, the Löwenheim-Skolem theorems, and the incompleteness of arithmetic. There is also a good sketch of more advanced topics, giving the enthusiastic reader and student incentive to keep studying the field. As with Professor Yaqub’s earlier logic text, An Introduction to Logical Theory, the presentation is clear and straightforward.” — Stewart Shapiro, Ohio State University “Yaqub has produced a pedagogically sensitive, yet completely rigorous tour of the introductory metalogical terrain. His textbook will be welcomed by instructors in philosophy, mathematics, computer science and linguistics who endeavor to offer their students something more substantial than standard introductory logic.” — Kai Wehmeier, University of California, Irvine

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Back cover copy

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between.

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About Aladdin M. Yaqub

Aladdin M. Yaqub is Associate Professor of Philosophy at Lehigh University.

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Table of contents

IntroductionChapter One: First-Order Predicate Logic1. The Syntax of PL2. The Semantics of PL3. Logical Concepts in PL4. PL Proof Theory5. ExercisesChapter Two: Resources of the Metatheory1. Linguistic and Logical Resources2. Arithmetical Resources3. Set-Theoretic Resources4. An Economical Version of PL5. ExercisesChapter Three: The Soundness and Completeness Theorems1. The Soundness Theorem2. The Completeness Theorem3. The Compactness Theorem4. PL Interpretations and PL Sets5. The Lowenheim-Skolem Theorem6. ExercisesChapter Four: Computability1. Effective Procedures and Computable Functions2. Turing Computability3. The Halting Problem4. Partial Recursive Functions5. ExercisesChapter Five: The Incompleteness Theorems1. Peano Arithmetic2. Representability in Peano Arithmetic3. The Arithmetization of the Metatheory4. Diagonalization and the First Incompleteness Theorem5. Consequences of Diagonalization and Incompleteness6. The Incompleteness of Second-Order Predicate Logic7. Godel's Second Incompleteness Theorem8. Exercises

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