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Quasivarieties of distributive lattices with a quantifier

✍ Scribed by M.E. Adams; W. Dziobiak

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
871 KB
Volume
135
Category
Article
ISSN
0012-365X

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✦ Synopsis

It is shown that any subvariety Y of the variety of bounded distributive lattices with a quantifier, as considered by Cignoli (1991), contains either uncountably or finitely many quasivarieties depending on whether Vcontains the 4-element bounded Boolean lattice with a simple quantifier. It is also shown that, in the former case, the quasivarieties contained in Yform a lattice which fails to satisfy every nontrivial lattice identity while, in the latter case, they form a chain of length < 3.

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