Title: On Inner Constructivizability of Admissible Sets
Abstract: We consider a problem of inner constructivizability of admissible
sets by means of elements of a bounded rank. For hereditary finite
superstructures we find a precise estimates for 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 field of real numbers has rank 1.
PDF