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On \(n\)-fold implicative filters of lattice implication algebras. (English) Zbl 0998.03508
Summary: We introduce the notion of \(n\)-fold implicative filters and \(n\)-fold implicative lattice implication algebras. We give characterizations of \(n\)-fold implicative filters and \(n\)-fold implicative lattice implication algebras. Finally, we construct an extension property for \(n\)-fold implicative filters.

MSC:
03G10 Logical aspects of lattices and related structures
06B10 Lattice ideals, congruence relations
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