= Solution
In the <Lévy hierarchy>, a <bounded formula in set theory> has only quantifiers of the forms $\forall x\in y$ and $\exists x\in y$. A <Sigma-one formula in set theory> is an existential unbounded quantifier block followed by a <bounded formula in set theory>, and a <Pi-one formula in set theory> has a universal unbounded block. \b[A formula is a <Delta-one formula modulo ZFC> if <ZFC> proves it equivalent, with the same free variables, both to a $\Sigma_1$ formula and to a $\Pi_1$ formula.] Equivalence modulo the specified theory is part of the definition; it is not necessary that the original string have both syntactic forms. Such formulas satisfy the usual <Delta-one absoluteness> between <transitive models> satisfying the relevant axioms. The modulo-ZF analogue is a <Delta-one formula in set theory>.
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