Streamlined subrecursive degree theory
The paper under review consists of two parts. Part I is devoted to the investigation of the structure of honest elementary degrees, i.e., the degree structure induced on the honest functions by the reducibility relation ``being (Kalmar) elementary in''. In Part II the degree theory found in Part I is generalized. The reducibility relation ``being \(\alpha\)-elementary in'', where \(\alpha\) is an ordinal \(\leq \varepsilon_{0}\), is introduced and the structure of honest \(\alpha\)-elementary degrees is investigated. Relations between the degree theory developed in the paper and provability in Peano arithmetic is also discussed.
scientific article; zbMATH DE number 6019358