Lévy hierarchy

English

Etymology

Introduced by Azriel Lévy in 1965.

Proper noun

the Lévy hierarchy

1. (set theory, logic) A hierarchy of formulas in the formal language of the Zermelo-Fraenkel set theory. Its first level contains only formulas with no unbounded quantifiers and is denoted by $\Delta _{0}=\Sigma _{0}=\Pi _{0}$. Subsequent levels are given by finding a formula in prenex normal form which is provably equivalent over ZFC, and counting the number of changes of quantifiers.