1. Structures and Languages.
Naively. Languages. Terms and Formulas. Induction. Sentences. Structures. Truth in a Structure. Substitutions and Substitutability. Logical Implication. Summing Up, Looking Ahead.
2. Deductions.
Naively. Deductions. The Logical Axioms. Rules of Inference. Soundness. Two Technical Lemmas. Properties of our Deductive System. Non-Logical Axioms. Summing Up, Looking Ahead.
3. Completeness and Compactness.
Naively. Completeness. Compactness. Substructures and the Loewenheim-Skolem Theorems. Summing Up, Looking Ahead.
4. Incompleteness-Groundwork.
Introduction. Language, Structure, Axioms of N. Recursive Sets and Recursive Functions. Recursive Sets and Computer Programs. Coding-Naively. Coding Is Recursive. Goedel Numbering. Goedel Numbers and N. NUM and SUB Are Recursive. Definitions by Recursion Are Recursive. The Collection of Axioms Is Recursive. Coding Deductions. Summing Up, Looking Ahead. Tables of D-Definitions.
5. The Incompleteness Theorems.
Introduction. The Self-Reference Lemma. The First Incompleteness Theorem. Extensions and Refinements of Incompleteness. Another Proof of Incompleteness. Peano Arithmetic and the Second Incompleteness Theorem. George Boolos on the Second Incompleteness Theorem. Summing Up, Looking Ahead.
Appendix: Set Theory.
Exercises.
