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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.
Aladdin M. Yaqub is Associate Professor of Philosophy at Lehigh University.
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 Loewenheim-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. Goedel's Second Incompleteness Theorem8. Exercises
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- ID: 9781554811717
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