Geodesic
On collection of all computable subsets on admissible sets
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 1-7

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We study the existence of computable numberings of the set of all $\Delta$-predicates over admissible sets. We construct an admissible set whose set of all $\Delta$-predicates fails to have such a numbering and give a series of examples of admissible sets in which such numberings exist. 
@article{SEMR_2008_5_a0,
     author = {V. G. Puzarenko},
     title = {On collection of all computable subsets on admissible sets},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1--7},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a0/}
}
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V. G. Puzarenko. On collection of all computable subsets on admissible sets. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 1-7. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a0/