Effective extendability and fixed points.
Thomas H. Payne · Notre Dame Journal of Formal Logic · 1973
Let a be any sequence and let φ l9 φ 2 , ... be a standard enumeration of the partial recursive functions.A p.r.f.δ is said to be a fixed-point algorithm for a if and only if δ(n) is an α-fixed point for φ n (i.e., ne Dom δ and a(δ(n)) = a(φ n (δ(n))) whenever ψ n is total), a has the effective fixed-point property if and only if a has a total fixed-point algorithm.The purpose of this paper is to show that the effective fixed-point property is more properly viewed as an extendability property since: