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On systems of congruences on principal filters of orthomodular implication algebras. (English) Zbl 1174.03030

Summary: Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of J.C.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.

MSC:

03G25 Other algebras related to logic
06C15 Complemented lattices, orthocomplemented lattices and posets
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