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A note on convex sublattices of lattices

Václav Slavík — 1995

Commentationes Mathematicae Universitatis Carolinae

Let C S u b ( K ) denote the variety of lattices generated by convex sublattices of lattices in K . For any proper variety V , the variety C S u b ( V ) is proper. There are uncountably many varieties V with C S u b ( V ) = V .

On the variety Csub ( D )

Václav Slavík — 1991

Commentationes Mathematicae Universitatis Carolinae

The variety of lattices generated by lattices of all convex sublattices of distributive lattices is investigated.

Incomparably continuable sets of semilattices

Jaroslav JežekVáclav Slavík — 2000

Mathematica Bohemica

A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.

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