**Instructor**: Yiannis N. Moschovakis, MS 6240, ynm@math.ucla.edu

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.*