 Some weaker subsystems of ZFC are used. Zermelo set theory, the system Z described above, is still studied. The further restriction of the axiom of separation to formulas in which all quantifiers are bounded in sets \((\Delta_0\) separation) yields “bounded Zermelo set theory” or “Mac Lane set theory”, so called because it has been advocated as a foundation for mathematics by Saunders Mac Lane (1986). It is interesting to observe that Mac Lane set theory is precisely equivalent in consistency strength and expressive power to TST with the Axiom of Infinity. Z is strictly stronger than Mac Lane set theory; the former theory proves the consistency of the latter. See Mathias 2001a for an extensive discussion.