Word.ws English Dictionary

Lévy hierarchy

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.

Proper noun

the Lévy hierarchy

  1. 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.

Origin of Lévy hierarchy

Introduced by Azriel Lévy in 1965.

Questions about Lévy hierarchy

What does Lévy hierarchy mean?
Lévy hierarchy means 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.
What part of speech is Lévy hierarchy?
Lévy hierarchy is a proper noun.

Words near Lévy hierarchy in the dictionary

  1. Lévy
  2. Lévy flight
  3. Lévy flights
  4. Lévy glass
  5. Lévy glasses
  6. Lévy hierarchy
  7. Lévy walk
  8. Lévy walks
  9. Lézignan-Corbières
  10. Lézinnes
  11. Lê Chân

Source and license

Adapted from Wiktionary: Lévy hierarchy (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “Lévy hierarchy.” Word.ws, https://word.ws/l%C3%A9vy_hierarchy. Based on Wiktionary, CC BY-SA 4.0.