Lévy hierarchy

The Lévy hierarchy classifies formulas of set theory by their alternations of unbounded quantifiers, ignoring bounded quantifiers of the forms

\forall x \in y

and

\exists x \in y

.

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- Delta-one formula in set theory Lévy hierarchy

Delta-one formula in set theory ( $Δ_{1}^{ZF}$ )

Δ_{1}^{ZF}

when ZF proves it equivalent both to a

Σ_{1}

formula and to a

Π_{1}

formula. Such formulas are absolute between suitable transitive models of finite fragments of ZF.

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