High Quality Content by WIKIPEDIA articles! In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice (with join and meet operations written ? and ? and with least element 0 and greatest element 1) equipped with a binary operation a>b of implication such that (a>b)?a ? b, and moreover a>b is the greatest such in the sense that if c?a ? b then c ? a>b. From a logical standpoint, A>B is by this definition the weakest proposition for which modus ponens, the inference rule A>B, A ? B, is sound. Equivalently a Heyting algebra is a residuated lattice whose monoid operation a•b is a?b; yet another definition is as a posetal cartesian closed category with all finite sums. Like Boolean algebras, Heyting algebras form a variety axiomatizable with finitely many equations. Данное издание представляет собой компиляцию сведений, находящихся в свободном доступе в среде Интернет в целом, и в информационном сетевом ресурсе "Википедия" в частности. Собранная по частотным...

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