Bounded Limit Recursiveness

Let X be a Turing oracle. A function f(n) is said to be boundedly limit recursive in X if it is the limit of an X-recursive sequence of X-recursive functions f̃(n, s) such that the number of times f̃(n, s) changes is bounded by a recursive function of n. Let us say that X is BLR-low if every function which is boundedly limit recursive in X is boundedly limit recursive in 0. This is a lowness property in the sense of Nies. These notions were introduced by Joshua A. Cole and the speaker in a recently submitted paper on mass problems and hyperarithmeticity. The purpose of this talk is to compare BLR-lowness to similar properties which have been considered in the recursion-theoretic literature. Among the properties discussed are: K-triviality, superlowness, jump-traceability, weak jump-traceability, total ω-recursive enumerability, array recursiveness, array jump-recursiveness, and strong jump-traceability.