  In this paper, we build Fidel-structures valued models following the
methodology developed for Heyting-valued models; recall that Fidel structures
are not algebras in the universal algebra sense. Taking models that verify
Leibniz law, we are able to prove that all set-theoretic axioms of ZF are valid
over these models. The proof is strongly based on the existence of
paraconsistent models of Leibniz law. In this setting, the difficulty of having
algebraic paraconsistent models of law for formulas with negation using the
standard interpretation map is discussed, showing that the existence of models
of Leibniz law is essential to getting models for ZF.
