Unfolding Schematic Systems

Abstract

The notion of unfolding a schematic formal system was introduced by Feferman in 1996 in order to answer the following question: Given a schematic system \(\mathsf {S}\), which operations and predicates, and which principles concerning them, ought to be accepted if one has accepted \(\mathsf {S}\)? After a short summary of precursors of the unfolding program, we survey the unfolding procedure and discuss the main results obtained for various schematic systems S, including non-finitist arithmetic, finitist arithmetic, feasible arithmetic, and theories of inductive definitions.