Mar 29, 2024  
2021 - 2022 Academic Catalog 
    
2021 - 2022 Academic Catalog [ARCHIVED CATALOG]

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 (together with applications to random graphs, algebraically closed fields, and nonstandard analysis). Finally, we will develop different ways to define the computable sets and functions, and end with a proof of the First Incompleteness Theorem. 

Prerequisite: MAT 321 . MAT 316  highly recommended.
Instructor: Mileti