Universal Pi^0_1 Classes

Series: Logic Seminar

Date: Tuesday, February 1, 2000

Speaker: Stephen G. Simpson (Penn State, Math)

Title: Universal Pi^0_1 Classes

Time: 2:30 - 3:20 PM

Place: 219 Thomas Building

Abstract: 

We consider nonempty Pi^0_1 subclasses of 2^omega.  Call a Pi^0_1
class P universal if for every Pi^0_1 class Q there exists a recursive
functional F : P --> Q.  We show that universal Pi^0_1 classes are
just the Stone spaces of Lindenbaum algebras of effectively
essentially undecidable theories.  We sketch the proof of a result of
Pour-El and Kripke: Any two universal Pi^0_1 classes are recursively
homeomorphic.