Retraceable Sets

Abstract

Let us compare two properties of sets of non-negative integers: (1) the set a has property Γ, if there exists an effective procedure which when applied to any element of a different from its maximum (which α does not necessarily possess) yields the next larger element of α; (2) the set α has property Δ, if there exists an effective procedure which when applied to any element of α different from its minimum yields the next smaller element of α. It is readily seen that every recursive set has both properties.