 It can also be considered as a theory in second-order logic, where now the separation axiom is just a single axiom.The second-order interpretation of Zermelo set theory is probably closer to Zermelo's own conception of it, and is stronger than the first-order interpretation.In the usual cumulative hierarchy "V"α of ZFC set theory (for ordinals α), any one of the sets
"V"α for α a limit ordinal larger than the first infinite ordinal ω (such as "V"ω·2) forms a model of Zermelo set theory.