Fall 2004 Peter Selinger |
1. Sept 9: Introduction, formal definition of PROP. 2. Sept 14: Informal logic: translations, truth tables. 3. Sept 16: Validity, logical implication. Induction principle. 4. Sept 23: Recursion principle. Uniqueness of parsing. Valuations. 5. Sept 24: Fitch style natural deduction. 6. Sept 28: Prawitz style natural deduction. 7. Oct 5: Analytic tableaux. 8. Oct 7: Soundness and completeness for analytic tableaux. 9. Oct 12: Soundness and completeness for natural deduction. 10. Oct 14: Completeness for natural deduction, continued. 11. Oct 19: Compactness theorem, applications of compactness. 12. Oct 21: Midterm 13. Oct 26: Predicate logic, variables, predicates, functions, structures 14. Oct 28: Translation, examples of interpretation in structures 15. Nov 2: Syntax: BNF, language of predicate logic, free and bound variables, substitution 16. Nov 4: Semantics: structures, interpretation, counterexamples 17. Nov 9: Properties of predicate logic 18. Nov 11: Fitch-style natural deduction for predicate logic 19. Nov 16: Analytic tableaux for predicate logic, Hintikka sets 20. Nov 18: Systematic tableaux, completeness, finite counterexamples 21. Nov 19: Henkin theories, conservative extensions 22. Nov 23: Lindenbaum's lemma, model construction, completeness, compactness 23. Nov 25: Non-standard models, non-standard arithmetic, non-standard reals 24. Nov 30: N.st. definition of continuity, Lowenheim-Skolem thm, finite models 25. Dec 2: Gödel's incompleteness theorem