This course provides an introduction to mathematical logic aimed at relatively advanced mathematics majors and mathematically inclined computer science and philosophy majors.
Part 1, Propositional logic: Syntax and semantics, Functional Completeness, Axiomatization and Deductive Completeness. About two weeks.
Lecture notes: The propositional calculus PL.
Part 2, First order logic: Syntax and semantics, elementary definability, arithmetical relations on the natural numbers, structures which admit quantifier elimination; the Completeness, Compactness and Skolem-Löwenheim Theorems. About six weeks.
Lecture notes: The lower predicate calculus with identity LPCI.
Part 3, Tarski's Theorem and the Gödel Incompleteness Theorem. About two weeks.
Lecture notes: The theorems of Tarski and Gödel.
Text: The course will be taught from Lecture Notes posted on the class homepage. If you want printouts of the notes, send me email.
Students who want to consult a supplementary textbook may look at An introduction to mathematical logic by Herbert Enderton.
Homework will be assigned on the class homepage and collected in the Section meeting every Tuesday. It will not be possible to accept late homework.
Grading. The grade will be based on two midterms (about 30% of
the grade), the final exam (about 40%) and the Homework, which
will count for 30%. The Final Exam may include a take-home part
in addition to the in-class part.
Fair warning. Math 114L is more difficult, it is more abstract and it covers substantially more material than the typical, upper division math course. It is especially fast-paced in the beginning, and if you stay behind in the first two weeks, you will never catch up.