Isomorphisms between HEO and HROE, ECF and ICFE

Journal of Symbolic Logic 50 (2):359 - 371 (1985)
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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"

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10.2307/2274222

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