MATH 4802
INTRODUCTION TO MATHEMATICAL LOGIC
Jan - April 2014
TEXT: Richard E. Hodel, "An Introduction to Mathematical Logic" Dover 2013.
One (instructor) copy will be in the CU Library on 24 hr Reserve.
MAJOR REFERENCE: on 24 hr reserve in the CU Library:
J.N. Crossley et al. “What is Mathematical Logic?” Dover 1990 (from OUP 1972),
Also available online at
http://books.google.ca/books?id=lywZ9zF3Yo4C&pg=PA11&source=gbs_toc_r&cad=4#v=onepage&q&f=false
INSTRUCTOR: Dr. John Poland, email: [email protected] , Office: #3-5250HP
website: tba
MARKING SCHEME:
Term work of weekly assignments: total 35% for best 7 of 10,
+ midterm test 30% Wed Feb 26 in class(90 minutes),
and final exam: 35%.
Final exam will be held on Monday April 7, 2 hours in class.
LECTURES: Mon & Wed 1:00 – 2:30 in 313SA. OFFICE HRS: Mon & Wed after class.
WEEKLY COURSE OUTLINE: Winter Term Jan - April
WEEK 1. (Jan 6&8/2014) Intro, review countable/uncountable, decidable and listable. Propositional calculus,
truth assignments, truth tables §2.1, 2.2 (Sections § as in the textbook).
WEEK 2. (J13&15)
WEEK 3. (J20&22) First-order languages, interpretations, models, eg; emphasize notation §1.4, 4.1, 4.2 .
WEEK 4. (J27&29) Truth, Satisfiability in Predicate Calculus, logically valid wff §4.3 .
WEEK 5. (F3&5) Definability and homomorphisms (handout extra to text). Elementary equivalence.
WEEK 6. (F10&12). Proof Theory: FOL, Axioms and Proofs, substitution and generalization. § 4.4, 5.1 .
(F16 to 20 is Reading Week.)
WEEK 7. (F24&26) Review for test. Test in class.
WEEK 8. (M3&5) Soundness, special lemmas, Model Existence Theorem. § 5.2, 5.3, 5.4 .
WEEK 9. (M10&12) More Model Existence Thm, Godel’s Completeness Thm, related algorithms § 5.4, 5.5 .
WEEK 10. (M17&19) Compactness Thm, Lowenheim-Skolem Thm, examples including Nonstandard Analysis. § 6.1, 6.2 .
WEEK 11. (M24&26) Gödel's Incompleteness Theorem. § 7.1, 7.2, 7.3 .
WEEK 12. (M31&A2) Gödel's Incompleteness Theorem. Review. § 7.4, (7.5, 7.6 lightly) .
WEEK 13. (A7) Final Exam in class; classes end April 8.
Because of the importance of the later topics, we will attempt not to linger over earlier topics.
Hence this Course Outline may proceed at a quicker pace than outlined above.