An Introduction to Metalogic

An Introduction to Metalogic

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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 | 310 pages
  • 178 x 226 x 18mm | 599.99g
  • Peterborough, Canada
  • English
  • 1554811716
  • 9781554811717
  • 979,535

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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Table of contents

Introduction
Chapter One: First-Order Predicate Logic
1. The Syntax of PL
2. The Semantics of PL
3. Logical Concepts in PL
4. PL Proof Theory
5. Exercises
Chapter Two: Resources of the Metatheory
1. Linguistic and Logical Resources
2. Arithmetical Resources
3. Set-Theoretic Resources
4. An Economical Version of PL
5. Exercises
Chapter Three: The Soundness and Completeness Theorems
1. The Soundness Theorem
2. The Completeness Theorem
3. The Compactness Theorem
4. PL Interpretations and PL Sets
5. The Loewenheim-Skolem Theorem
6. Exercises
Chapter Four: Computability
1. Effective Procedures and Computable Functions
2. Turing Computability
3. The Halting Problem
4. Partial Recursive Functions
5. Exercises
Chapter Five: The Incompleteness Theorems
1. Peano Arithmetic
2. Representability in Peano Arithmetic
3. The Arithmetization of the Metatheory
4. Diagonalization and the First Incompleteness Theorem
5. Consequences of Diagonalization and Incompleteness
6. The Incompleteness of Second-Order Predicate Logic
7. Goedel's Second Incompleteness Theorem
8. Exercises
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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 Lowenheim-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 "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 Loewenheim-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 Comments:

"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 Loewenheim-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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About Aladdin M. Yaqub

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