The theory of quasivarieties constitutes an independent direction in algebra and
mathematical logic and specializes in a fragment of first-order logic-the so-called universal …

This text explores the surprisingly complex structure of free lattices. The first part of the book
presents a complete exposition of the basic theory of free lattices, projective lattices, and …

Closure systems (ie families of subsets of a set S containing S and closed by set
intersection) or, equivalently, closure operators and full implicational systems appear in …

We introduce the notion of a convex geometry extending the notion of a finite closure system
with the anti-exchange property known in combinatorics. This notion becomes essential for …

The book Roads to Quoz, by William Least Heat-Moon, describes that author's search for the
mysterious reward that awaits the curious traveler, as much in the journey as the destination …

Nearly twenty years ago, two of the authors wrote a paper on congruence lattices of
semilattices [9]. The problem of finding a really useful characterization of congruence lattices …

Finite atomistic lattices that can be represented as lattices of quasivarieties Page 1
FUNDAMENTA MATHEMATICAE 142 (1993) Finite atomistic lattices that can be …

Abstract The Gorbunov-Tumanov conjecture on the structure of lattices of quasivarieties is
proved true for the case of algebraic lattices. Namely, for an algebraic atomistic lattice L, the …

For any ordered set P, the join dense completions of P form a complete lattice K (P) with
least element O (P), the lattice of order ideals of P, and greatest element M (P), the Dedekind …

Implicational bases (IBs) are a common representation of finite closure systems and lattices,
along with meet-irreducible elements. They appear in a wide variety of fields ranging from …