Halaš, Radomír; Plojhar, Luboš On systems of congruences on principal filters of orthomodular implication algebras. (English) Zbl 1174.03030 Math. Bohem. 132, No. 4, 423-435 (2007). 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. Cited in 1 Document MSC: 03G25 Other algebras related to logic 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:orthoimplication algebra; orthomodular lattice; \(p\)-filter PDF BibTeX XML Cite \textit{R. Halaš} and \textit{L. Plojhar}, Math. Bohem. 132, No. 4, 423--435 (2007; Zbl 1174.03030) Full Text: EuDML EMIS