Pseudocomplemented and Implicative Semilattices

Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 423-437

Résumé

Let L be a semilattice and let a ∊ L. We refer the reader to Definitions 2.2, 2.4, 2.5 and 2.12 below for the terminology. If L is a-implicative, let Ca be the set of a-closed elements of L, and let Da be the filter of a-dense elements of L. Then Ca is a Boolean algebra. If a = 0, then C 0 and D 0 are the usual closed algebra and dense filter of L. If L is a-admissible and f : Ca × Da → Da is the corresponding admissible map, we can form a quotient semilattice Ca × D 0 f. In case a = 0, Murty and Rao [4] have shown that C 0 × D 0/f is isomorphic to L, and hence that C 0 × D 0 is 0-admissible. In case L is in fact implicative, Nemitz [5] has shown that C 0 × D 0/f is isomorphic to L, and that C 0 × D 0/f is also implicative.

Détail

DOI : 10.4153/CJM-1982-028-6

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