Friedberg Numbering in Fragments of Peano Arithmetic andα-Recursion Theory
Wei Li · Journal of Symbolic Logic · 2013
Abstract In this paper, we investigate the existence of a Friedberg numbering in fragments of Peano Arithmetic and initial segments of Gödel's constructible hierarchyLα, whereαis Σ1admissible. We prove that (1) OverP−+BΣ2, the existence of a Friedberg numbering is equivalent toIΣ2, and (2) ForLα, there is a Friedberg numbering if and only if the tame Σ2projectum ofαequals the Σ2cofinality ofα.