Dumitru Busneag and Mircea Ghita: Some latticial properties of Hilbert algebras. p.87-107

Abstract:

The aim of this paper is to study some properties of Hilbert
algebras relative to the natural order. Connections between Hilbert algebras with infimum and Hertz algebras are made. For the case of Hilbert algebras with supremum is offered an equational characterization. Afterwards, some rules of calculus for Hilbert algebras with a latticeal structure are provided and a result from [14] relative to implicative semilattices is improved and generalized to the case of Hilbert algebras with infimum.

Key Words: Hilbert algebra, Heyting algebra, Hilbert algebra with infimum, Hilbert algebra with supremum, Hertz algebra, semi-Boolean lattices, semi-Boolean Hilbert algebra.

2000 Mathematics Subject Classification: Primary: 03G10,
Secondary: 03G25, 06A12, 06D20, 06F35.

Download the paper in pdf format here.