Abstract

In this paper it will be shown that HEO and $HRO^E$ are isomorphic with respect to extensional equality. This answers a question of Troelstra [T, 2.4.12, p. 128]. The main problem is to extend effective operations to a larger domain. This will be achieved by a modification of the proof of the continuity of effective operations. Following a suggestion of A.S. Troelstra, similar results were obtained for ECF(U) and $ICF^E(U)$, where $U$ is any universe of functions closed under "recursive in"