Some restrictions on simple fixed points of the integers

A function is recursive (in given operations) if its values are computed explicitly and uniformly in terms of other “previously computed” values of itself and (perhaps) other “simultaneously computed” recursive functions. Here, “explicitly” includes definition by cases. We investigate those recursive functions on the structure N = 〈 ω , 0, succ, pred〉 that are computed in terms of themselves only, without other simultaneously computed recursive functions.