On Pre-Hilbert and Positive Implicative Pre-Hilbert Algebras
On Pre-Hilbert and Positive Implicative Pre-Hilbert Algebras

Summary/Abstract: In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin’s Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.

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