MATH 7830: Model Theory (Spring 2010)

Instructor: Justin Moore

Model theory is the abstract study of structures. This course will provide a fast-paced and modern introduction to the subject, emphasizing examples arising in commutative algebra.

This course will begin with a review of Henkin's construction and proceed through the following topics: compactness and completeness, the Lowenheim-Skolem theorems, back and forth arguments, quantifier elimination, the space of types, indiscernibles, homogeneity, saturation, simple theories, and categoricity. The culmination of the course will be Morley's Categoricity Theorem.

I will teach out of Marker's book, which emphasizes examples arising from algebra. The intended audience is both students in logic and students in algebra interested in a different perspective of their subject. Students are expected to have some comfort level with predicate logic (at the level of Chapter 1 of Marker's book), but there is no formal prerequisite for this course. Students will also benefit from having taken an algebra course at either the advanced undergraduate level or beginning graduate level.