MATH 7830 - Model Theory

Justin Moore, spring 2014.

Model theory is the abstract study of structures. This course will provide a modern introduction to the subject, emphasizing the algebraic aspects of the subject.

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. 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.