Isomorphisms Between HEO and $\mathrm{HRO}^\mathrm{E}$, ECF and $\mathrm{ICF}^\mathrm{E}$
Bezem, Marc
J. Symbolic Logic, Tome 50 (1985) no. 1, p. 359-371 / Harvested from Project Euclid
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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".
Publié le : 1985-06-14
Classification:  
@article{1183741840,
     author = {Bezem, Marc},
     title = {Isomorphisms Between HEO and $\mathrm{HRO}^\mathrm{E}$, ECF and $\mathrm{ICF}^\mathrm{E}$},
     journal = {J. Symbolic Logic},
     volume = {50},
     number = {1},
     year = {1985},
     pages = { 359-371},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741840}
}

Bezem, Marc. Isomorphisms Between HEO and $\mathrm{HRO}^\mathrm{E}$, ECF and $\mathrm{ICF}^\mathrm{E}$. J. Symbolic Logic, Tome 50 (1985) no. 1, pp.  359-371. http://gdmltest.u-ga.fr/item/1183741840/