EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 28(42), pp. 25--32 (1980)

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TRUTH FILTERS IN DE MORGAN LATTICES

Milan Bozi\'c

Matematicki fakultet, Beograd, Yugoslavia

Abstract: In this paper Stone-type theorems on existence of truth filters in De Morgan lattices are obtained. It is shown that $(^*)\cdots(a\wedge T)\cap T_0=\emptyset$ is necessary and sufficient for existence of a truth filter containing {\bf a}, where $T_0$ and $T_1$ are sets of zeroes and units. Also, it is proved that the filter $F$ is contained in a truth filter iff for each member {\bf a} of $F$ holds $(^*)$. Some other related results are proved, too.

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