Cancelling Congruences of Lattices, While Keeping Their Numbers of Filters and Ideals

Abstract

In this paper, we study the congruences, prime filters and prime ideals of horizontal sums of bounded lattices, then, through a construction based on horizontal sums and without enforcing the Continuum Hypothesis, we are modifying an example from \cite{eucard} into a solution to the problem we have proposed in the same article: finding a lattice with the cardinalities of the sets of filters, ideals and congruences pairwise distinct.