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

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