Meeting: Association for Symbolic Logic 2007 Annual Meeting Gainesville, Florida March 10-13, 2007 Session: Special Session on Computability Organized by Noam Greenberg Speaker: Stephen G. Simpson Address: Department of Mathematics Pennsylvania State University McAllister Building, University Park State College, PA 16802, USA E-mail: t20@psu.edu Title: Bounded Limit Recursiveness Abstract: 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 f(n,s) such that the number of times f(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 omega-recursive enumerability, array recursiveness, array jump-recursiveness, and strong jump-traceability.