Courses

Proves the compactness theorem, showing the essential finiteness of logical implication. Proves many basic properties of theories, showing how the syntactic form of statements influences their behavior w.r.t, different models. Finally, studies properties of elements that cannot be stated by a single formula (the type of the element) and shows it can be used to characterize certain models. Prerequisites: Restricted to Graduate Students only.

Studies the computable and uncomputable. Shows that there are undecidable problems, and from there builds up the theory of sets of natural numbers under Turing reducibility. We will study Turing reducibility, the arithmetical hierarchy, oracle constructions, and end with the finite injury priority method. Recommended prereq., MATH 6000. Prerequisites: Restricted to Graduate Students only.