Abstract

We examine the action of unary Δ 0 2 functions on the regressive isols. A manageable theory is produced and we find that such a function maps Λ R into Λ if and only if it is eventually $R\uparrow$ increasing and maps Λ R into Λ R if and only if it is eventually recursive increasing. Our paper concludes with a discussion of other methods for extending functions to Λ R