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Heyting algebra

Heyting algebra noun: a bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).

Noun

Heyting algebra (plural Heyting algebras)

  1. A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).
    • The laws of Heyting algebra embody a rich and profound mathematical structure that is manifest in a variety of contexts. It arises from the epistemological deliberations of Brouwer, the topologisation (localisation) of set-theoretic notions, and the categorial formulation of set theory, all of...1984, Robert Goldblatt, Topoi, the categorial analysis of logic, page xii
    • which is just obvious.1994, Francis Borceux, Handbook of Categorical Algebra 3: Categories of Sheaves, Cambridge University Press, page 13, Proposition 1.2.14 should certainly be completed by the observation that the...
    Synonyms:
    pseudo-Boolean algebra

Synonyms of Heyting algebra

  • pseudo-Boolean algebra

Forms of Heyting algebra

pluralHeyting algebras

Origin of Heyting algebra

After Dutch mathematician Arend Heyting, who developed the theory as a way of modelling his intuitionistic logic.

Words formed from Heyting algebra

  • bi-Heyting algebra
  • biHeyting algebra
  • co-Heyting algebra
  • coHeyting algebra
  • complete Heyting algebra

Questions about Heyting algebra

What does Heyting algebra mean?
Heyting algebra means a bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).
What part of speech is Heyting algebra?
Heyting algebra is a noun.
What is the plural of Heyting algebra?
The plural of Heyting algebra is Heyting algebras.

Words near Heyting algebra in the dictionary

  1. Heystek
  2. Heysteks
  3. Heytesbury
  4. Heytesbury Lower
  5. Heyting
  6. Heyting algebra
  7. Heyting algebras
  8. Heyuan
  9. Heyward
  10. Heywood
  11. Heywood Jablome

Source and license

Adapted from Wiktionary: Heyting algebra (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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