An Introduction to Metalogic

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 Lowenheim-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. Godel's Second Incompleteness Theorem 8. Exercises