MATH 781: Logic Seminar (Fall 2005)

Instructor: Richard Shore

Meeting Time & Room

As usual the seminar will focus on a special topic one day a week. Participants will take turns lecturing. The other day will be devoted to a variety of topics depending on the interests and research activities of the participants and will include some outside speakers as well.

There are two possibilities for the topic for 781 this term.

If we do not do hyperarithmetic theory in 784 we will do it in 781 using Higher Recursion Theory by Gerald Sacks.

This begins with the constructive ordinals, effective transfinite recursion and Pi-1-1 sets. Then an analysis of the hyperarithmetic hierarchy based on iterating the Turing jump into the transfinite. Included is the equivalence of HYP and Delta-1-1 (which is the effective analog of Borel = analytic and coanalytic). Next is a deeper analysis of analytic (=Sigma-1-1=projections of Borel) and coanalytic (=Pi-1-1=complements of analytic) sets. Basis theorems, uniformization, selection and the perfect set theorem. If this topic is not covered in 784 it will be the topic for 781.

Otherwise, we will do effective model theory using article in the Handbook of Recursive Mathematics vol. 1 (Ershov, Goncharov, Nerode and Remmel eds.) and the book Computable Structures and the Hyperarithmetical Hierarchy by Ash and Knight.

People with preferences should contact me but the final choice may depend on who shows up for the courses in the fall.

Last modified: March 31, 2005