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

Halaš, Radomír; Plojhar, Luboš

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.

MSC:

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

Keywords:

orthoimplication algebra; orthomodular lattice; \(p\)-filter