= Definable continuous hierarchy
{title2=$H_\lambda=\bigcup_{\alpha<\lambda}H_\alpha$}
= Hierarchy in set theory
{synonym}
A definable continuous hierarchy is a definable class function from the <ordinals> to <sets>, with increasing levels $H_\alpha$ and the displayed continuity condition at nonzero <limit ordinals>. Its union is a definable <class in set theory>. One often additionally requires <transitive sets> as levels. Finite collections of <first-order formulas> reflect along this hierarchy by the <reflection theorem for definable hierarchies>.
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