Quantum B-algebras: their omnipresence in algebraic logic and beyond
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Quantum B-algebras are implicational subreducts of quantales. Their ubiquity and unifying rôle in algebraic logic and beyond is discussed in a brief survey, with old and new examples included. A special section is devoted to CKL-algebras (alias HBCK-algebras). Using a natural embedding of any CKL-algebra into a semibrace, Cornish’s identity is derived, which yields a new syntactic proof of Wroński’s conjecture that CKL-algebras form a variety.