Splinters of recursive functions

Abstract

Basic notation in this paper is as in [3]. From [5] and [9] the following additional notation is derived,ϕiis the partial recursive function with indexi, Wiits range. ∅ is the empty set. ‘≡’ denotes isomorphism between sets, ‘≡m’ many-one equivalence, ‘≡T’ Turing equivalence, ‘≦1’ and ‘≦m’ signify one-one and many-one reducibility respectively. ‘Recursive’ is used throughout for ‘general recursive’.