Math 783 — Spring 2002 Model Theory

Model theory explores the mathematical relationships between syntax (the language used to express mathematical statements) and semantics (the actual structures about which we make these statements). Specific topics we will cover include completeness and compactness; nonstandard models; the Lowenheim-Skolem-Tarski theorems; homomorphisms of structures; elementary equivalence; realizing and omitting types; prime, atomic, homogeneous, and saturated models; back-and-forth constructions and Ehrenfeucht games; amalgamations and Fraisse theory; categoricity of models; and ultraproducts. Depending on time and the inclinations of the class, we may also cover indiscernibles, Lindstrom's Theorem, computable model theory, decidability, interpretations of models, and/or model completeness. The text for the course will be Wilfrid Hodges's Model Theory; a secondary reference is the book of the same title by Chang and Keisler.

This course will assume reasonable familiarity with basic logic. Math 681 or a similar course is ample. Prospective students with questions about the course are encouraged to talk to the instructor.