ABSTRACT
Definition 1.1. The real A is super-low if g(e , s) for a computable 0 ,1-valued g such that g{e, s) changes at most
b(e) times, for a computable function b. This notion goes back to work of Mohrherr [8], and an unpublished man
uscript of Bickford and Mills [1] (where only super-low r.e. sets are studied, called “abject” there). The canonical construction of a low simple set (see [10, Theorem VII. 1.1]) produces in fact a super-low set: one satisfies lowness requirements
closed under Turing reducibility , and that each real A with that property is generalized low, namely In this paper we study and compare
the halting problem for a computable
Equivalently, lim
is injured at most e times by requirements
tion 3.1 below).
