MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 423-435 (2007)

On systems of congruences on principal filters of orthomodular implication algebras

Radomir Halas, Lubos Plojhar

Radomir Halas, Lubos Plojhar, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: halas@inf.upol.cz, plojhar@inf.upol.cz

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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