ONTIC: A Knowledge Representation System for Mathematics by McAllester, David Allen

“…Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. …”
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Hierarchies Ontological and Ideological by Linnebo, Oystein

“…Godel claimed that Zermelo-Fraenkel set theory is `what becomes of the theory of types if certain superfluous restrictions are removed'. …”
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Bi-interpretation in weak set theories by Freire, AR, Hamkins, JD

“…Nevertheless, for natural weaker set theories, we prove, including Zermelo-Fraenkel set theory ZFC− without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. …”

The Iterative Conception of Set by Studd, J

“…It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo-Fraenkel set theory. © 2012 Springer Science+Business Media B.V.…”

Absolute and relative generality by Studd, JP

“…Chapter 5 argues that relativism permits a natural motivation for Zermelo-Fraenkel set theory. A new, bi-modal axiomatisation of the iterative conception of set is presented. …”

Ontology and the foundations of mathematics by Uzquiano, Gabriel, 1968-

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