Radomir Halas, Lubos Plojhar, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: email@example.com, firstname.lastname@example.org
Abstract: Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott's implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.
Keywords: orthoimplication algebra, orthomodular lattice, $p$-filter
Classification (MSC2000): 03B60, 06B10, 06C15
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