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Representation of Hilbert algebras and implicative semilattices. (English) Zbl 1034.03056

Summary: We give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego [Sur les algèbres de Hilbert. Paris: Gauthier-Villars (1966; Zbl 0144.00105)]. For implicative semilattices this representation gives a full duality. We also consider the representation for Boolean rings.

MSC:

03G25 Other algebras related to logic
06A12 Semilattices
06E15 Stone spaces (Boolean spaces) and related structures

Citations:

Zbl 0144.00105
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References:

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