  What is the slightest modification of ZF to add a complement-axiom? The
answer in my Ph.D. thesis 1971 was ZF'': Zermelo-Fraenkel with replacement for
only well-founded domains and an omega-axiom. In 1974, Alonzo Church published
a similar system, as did Urs Oswald in 1976. In his 1976 Ph.D. thesis, E.
Mitchell also designed, a system very similar to ZF''. In this article we argue
that ZF'' is the slightest modification of ZF among all these systems and that
its successor ZFK is the simplest set theory with a universal set at all.
