Heyting algebra

名词 n.
中文释义

英文释义

名词 n.
  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 which, although interrelated, are independently motivated. The ubiquity lends weight, not to the suggestion that the correct logic is in fact intuitionistic instead of classical, but rather to the recognition that thinking in such terms is simply inappropriate — in the same way that it is inappropriate to speak without qualification about the correct geometry.

词形变化

Heyting algebras plural

词源

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