Geodesic
Commutative directoids with sectionally antitone bijections
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 1, pp. 77-89

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We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
Keywords: directoid, section antitone bijection, implication algebra, double implication algebra 
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Chajda, Ivan; Kolařík, Miroslav; Radeleczki, Sándor. Commutative directoids with sectionally antitone bijections. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 1, pp. 77-89. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_1_a4/