On tightly \(\kappa \)-filtered Boolean algebras.
In the paper the concept of tight \(\kappa \)-filteredness of a Boolean algebra for infinite regular cardinals \(\kappa \) is introduced and studied. Characterizations of tightly \(\kappa \)-filtered Boolean algebras which generalize the internal characterizations of projectivity are given. It is shown that for each \(\kappa \) there is an rc-filtered Boolean algebra that is not tightly \(\kappa \)-filtered. This generalizes a result of E. V. Ščepin. It is proved that no complete Boolean algebra of size larger than \(\aleph _{2}\) is tightly \(\aleph _{1}\)-filtered.
scientific article; zbMATH DE number 2158767