Principles of partial reflection in the set theories of zermelo and ackermann

It was shown in [4] that the Zermelo-Fraenkel set theory may be obtained by adjoining to the Zermelo theory Z an axiom schema called the principle of complete reflection. (This schema, denoted here by CR, and other notions involved in these introductory remarks will be described explicitly later.) A schema of partial reflection, called here PR, which is also valid in ZF was described in [5], As we shall see in §2, the theory T₀ = Z + PR is a very strong one, in which, apparently, all of the ‘ordinary’ set-theoretical constructions can be carried out.