FRIEDBERG NUMBERING IN FRAGMENTS OF PEANO ARITHMETIC AND α-RECURSION THEORY

摘要

In this paper, we investigate the existence of a Friedberg numbering in fragments of Peano Arithmetic and initial segments of G?del's constructible hierarchy L_α, where α is Σ_1 admissible. We prove that (1) Over P? + BΣ_2, the existence of a Friedberg numbering is equivalent to IΣ_2, and (2) For Lα, there is a Friedberg numbering if and only if the tame Σ_2 projectum of α equals the Σ_2 cofinality of α.