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


  Title:   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 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.