Max and min limiters

If A ⊆ ω, n ≥ 2, and the function max({x1, . . . , xn} ∩ A) is partial recursive, it is easily seen that A is recursive. In this paper, we weaken this hypothesis in various ways (and similarly for “min” in place of “max”) and investigate what effect this has on the complexity of A. We discover a sharp contrast between retraceable and coretraceable sets, and we characterize sets which are the union of a recursive set and a co-r.e., retraceable set. Most of our proofs are noneffective. Several open questions are raised.