Kentaro Fujimoto (Bristol University)
The Uniform Reflection Principle for Predicativity.
Abstract: Feferman formulated a variety of formal systems in an attempt to vindicate his life-long conviction that the Feferman-Schuette ordinal is the predicative limit. Among them is the system of the schematic reflective closure of Peano Arithmetic PA. According to him, the engines for systematically generating larger and larger systems whose acceptability is implicit in acceptance of the starting theory are what have come to be called reflection principles, and one of the main purposes of his schematic reflective closures is “to give a more perspicuous generation procedure for predicativity" without use of progression of those reflection principles. In this talk, I will examine Feferman's concept of schematic reflective closure, consider a theory for predicativity directly in terms of the reflection principles, and then investigate how these two kinds of theories are related.