MAT 444-01 - Senior Seminar: Mathematical Logic

4 credits (Spring)

The study of first-order logic using the tools of mathematics, together with applications of first-order logic to mathematics itself. We will study both syntactic and semantic notions of implication, and prove the Soundness and Completeness theorems connecting these concepts. We will also explore basic model theory, such as definability, back-and-forth arguments, and the Lowenheim-Skolem theorem. Applications to random graphs, algebraically closed fields, and nonstandard analysis will be included. Finally, we will develop some axiomatic set theory (with an emphasis on ordinals, cardinals, and the Axiom of Choice), and end with a discussion of the First Incompleteness Theorem.

Prerequisite: MAT 321. MAT 316 is also strongly recommended.
Instructor: Mileti