Lévy hierarchy

proper noun

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 Δ₀=Σ₀=Π₀. 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.

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Meanings

proper nounthe Lévy hierarchy
  1. human sciencesA 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 Δ₀=Σ₀=Π₀. 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.

Origin

Introduced by Azriel Lévy in 1965.

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Cite this entry
APA

Lévy hierarchy. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/L%C3%A9vy%20hierarchy

MLA

“Lévy hierarchy.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/L%C3%A9vy%20hierarchy. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Lévy hierarchy,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/L%C3%A9vy%20hierarchy.

Source: Lévy hierarchy on Wiktionary, CC BY-SA 4.0.