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 of the rank of inner
constructivizability: it is equal to $\omega$ for superstructures
over finite structures and less or equal to 2 otherwise. We
introduce examples of hereditary finite superstructures with ranks
0, 1, 2. It is shown that hereditary finite superstructure
over the field of real numbers has rank 1.