One The Propositional Calculus. - 1. Propositional Connectives. Truth Tables. - 2. Tautologies. - 3. Adequate Sets of Connectives. - 4. An Axiom System for the Propositional Calculus. - 5. Independence. Many-Valued Logics. - 6. Other Axiomatizations. - Two Quantification Theory. - 1. Quantifiers. - 2. Interpretations. Satisfiability and Truth. Models. - 3. First-Order Theories. - 4. Properties of First-Order Theories. - 5. Additional Metatheorems and Derived Rules. - 6. Rule C. - 7. Completeness Theorems. - 8. First-Order Theories with Equality. - 9. Definitions of New Function Letters and Individual Constants. - 10. Prenex Normal Forms. - 11. Isomorphism of Interpretations. Categoricity of Theories. - 12. Generalized First-Order Theories. Completeness and Decidability. - 13. Elementary Equivalence. Elementary Extensions. - 14. Ultrapowers. Nonstandard Analysis. - 15. Semantic Trees. - Three Formal Number Theory. - 1. Axiom System. - 2. Number-Theoretic Functions and Relations. - 3. Primitive Recursive and Recursive Functions. - 4. Arithmetization. Gödel Numbers. - 5. The Fixed Point Theorem. Gödel's Incompleteness Theorem. - 6. Recursive Undecidability. Church's Theorem. - Four Axiomatic Set Theory. - 1. An Axiom System. - 2. Ordinal Numbers. - 3. Equinumerosity. Finite And Denumerable Sets. - 4. Hartogs' Theorem. Initial Ordinals. Ordinal Arithmetic. - 5. The Axiom of Choice. The Axiom of Regularity. - 6. Other Axiomatizations of Set Theory. - Five Effective Computability. - 1. Algorithms. Turing Machines. - 2. Diagrams. - 3. Partial Recursive Functions. Unsolvable Problems. - 4. The Kleene-Mostowski Hierarchy. Recursively Enumerable Sets. - 5. Other Notions of Effective Computability. - 6. Decision Problems. - Answers to Selected Exercises. - Notation. Language: English