We prove that, under the Generalized Continuum Hypothesis, an infinite bounded involution lattice can have any number of (involution preserving lattice) congruences between 2 and its number of subsets, regardless of its number of ideals.

PBZ ∗ –lattices are bounded lattice–ordered structures endowed with two complements, called Kleene and Brouwer; by definition, they are the paraorthomodular Brouwer–Zadeh lattices in which the pairs… Expand

By a twenty year old result of Ralph Freese, an $n$-element lattice $L$ has at most $2^{n-1}$ congruences. We prove that if $L$ has less than $2^{n-1}$ congruences, then it has at most $2^{n-2}$… Expand

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this… Expand

I First Concepts.- 1 Two Definitions of Lattices.- 2 How to Describe Lattices.- 3 Some Algebraic Concepts.- 4 Polynomials, Identities, and Inequalities.- 5 Free Lattices.- 6 Special Elements.-… Expand