The notion of absolute independence, considered in this paper has a clear algebraic meaning and is a strengthening of the usual notion of logical independence. We prove that any consistent and countable set in classical prepositional logic has an absolutely independent axiornatization.

We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.

In this paper we will prove that ifF is a filter of a free Boolean algebra such that the minimal cardinality of the set of generators ofF is an uncountable regular cardinal or a singular cardinal with uncountable cofinality thenF is freely generated.

Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.