Lévy hierarchy

English

Etymology

Introduced by Azriel Lévy in 1965.

Proper noun

1. Template:Lb 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 ${\mathrm{\Delta }}_0={\mathrm{\Sigma }}_0={\mathrm{\Pi }}_0$. 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.