This is an introductory graduate course in mathematical logic. We will discuss each of the four main subjects of logic: set theory, model theory, proof theory, and computability theory. The main topics will include the axioms of Zermelo-Fraenkel set theory with choice, ordinal and cardinal arithmetic, the syntax and semantics of first-order logic, a first-order proof calculus, the Completeness and Compactness Theorems, the Löwenheim-Skolem Theorems, and the Incompleteness Theorems.
UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI 53706