Contents

• Contents
• Gödelian Preview
  • The First Puzzle
    • Exercises
    • Solutions
  • A Second Puzzle
    • Exercises
• Preliminaries
  • Essential Logic
  • Sets
  • Relations and Functions
  • Finite and Infinite Sets and Alphabets
    • Exercises
• Propositional Languages
  • Syntax
  • Semantics
  • Proof Theory
    • A Fitch-style Proof Theory
    • Resolution
    • Strategic Resolution and OTTER
  • Metatheory
    • Soundness
    • Completeness
• First-Order Languages
  • Syntax
  • Semantics
    • Satisfaction
    • Consequence and Other Concepts
  • Proof Theory
    • Natural Deduction
    • Resolution
  • Metatheory
    • Soundness
    • Completeness
    • The Löwenheim-Skolem Theorem
• Turing Machines
  • Definitions
  • Examples
  • The Halting Problem
  • The Undecidability of First-Order Logic
• Gödel's First Incompleteness Theorem
• Set Theory
  • Russells's Paradox
  • Axiomatic Set Theory
    • Zermelo-Fraenkel Axioms for Set Theory
  • The Continuum Hypothesis