Pi-0-1 classes, computable combinatorics, and effective Ramsey theory

			Carl G. Jockusch, Jr.

			University of Illinois

Pi-0-1 classes may be thought of as effectively closed sets in Cantor
or Baire space.  I will discuss basis and "antibasis" theorems for
Pi-0-1 classes in Cantor space and their connection with problems
in combinatorics and logic, including some open problems on
representing Pi-0-1 classes by decompositions of partial orderings.
Pi-0-1 classes are also closely related to Scott sets and the study of
the consequences of Weak Konig's Lemma.  Finally, I will review some
old and new results in effective Ramsey theory and mention some open
questions.  For example, it is not known whether Ramsey's theorem for
pairs implies Weak Konig's Lemma in the weak base theory RCA_0.