Complete Lattices Represent Complete Heyting Algebras (or: Quantum Logic with an Intuitionistic Implication)
نویسنده
چکیده
Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL. If L is itself a complete Heyting algebra then DI(L) ∼= L and RL = idDI(L). Ortholattices can similarly be represented bijectively (up to isomorphism) by complete Heyting algebras equipped with a disjunctive join dense pseudo-orthocomplementation.
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