S is an axiomatic set theory set out by George Boolos in his article, Boolos (1989). S, a first-order theory, is two-sorted because its ontology includes “stages” as well as sets. Boolos designed S to embody his understanding of the “iterative conception of set“ and the associated iterative hierarchy. S has the important property that all axioms of Zermelo set theory Z, except the axiom of Extensionality and the axiom of Choice, are theorems of S or a slight modification thereof.