Proof theory for theories of ordinals II: Π3-reflection

This paper deals with a proof theory for a theory T3 of Π3-reflecting ordinals using the system O(Π3) of ordinal diagrams in Arai (J. Symbolic Logic 65 (2000) 1375). This is a sequel to the previous one (Ann. Pure Appl. Logic 122 (2003) 1) in which a theory for recursively Mahlo ordinals is analyzed proof-theoretically.