Geodesic
On inner constructivizability of admissible sets
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 1, pp. 69-76

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We consider a problem of inner constructivizability of admissible sets by means of elements of a bounded rank. For hereditary finite superstructures we find the precise estimates for the rank of inner constructivizability: it is equal $\omega$ for superstructures over finite structures and less or equal 2 otherwise. We introduce examples of structures with hereditary finite superstructures with ranks 0, 1, 2. It is shown that hereditary finite superstructure over field of real numbers has rank 1. 
@article{VNGU_2005_5_1_a6,
     author = {A. I. Stukachev},
     title = {On inner constructivizability of admissible sets},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {69--76},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2005_5_1_a6/}
}
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A. I. Stukachev. On inner constructivizability of admissible sets. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/VNGU_2005_5_1_a6/