Constructing a Lattice With the Cardinalities of the Sets of Congruences, Filters and Ideals Pairwise Distinct
Claudia Mureșan · arXiv (Cornell University) · 2017
In this paper, I am giving a solution to the problem I have proposed in [eucard]: finding a lattice with the cardinalities of the sets of filters, ideals and congruences pairwise distinct; I am constructing such a lattice by using horizontal sums, and without enforcing the Continuum Hypothesis. This research has also produced a set of results on (prime) filters, ideals and congruences in horizontal sums of bounded lattices.