Heyting-algebra meaning

A bounded lattice equipped with a binary operation ab of implication such that (ab)∧ab, and moreover ab is the greatest such in the sense that if cab then cab.

If the less-than-or-equal relation in the definition of Heyting algebra is interpreted to mean logical entailment, then (a→b)∧a ≤ b translates to "(a→b), a ⊢ b" which is Modus Ponens. The formulae in the second condition translate to "c, a ⊢ b ⇒ c ⊢ a→b" which is the Deduction Theorem.

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Boolean algebra.
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Complete Heyting algebra.
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Origin of heyting-algebra

  • After Arend Heyting.
    From Wiktionary