I’ve proved: There exists a filter which cannot be (both weakly and strongly) partitioned into ultrafilters. It is an easy consequence of a lemma proved by Niels Diepeveen (also Karl Kronenfeld has helped me to elaborate the proof). See the preprint of…

read moreI uploaded updated version of Filters on Posets and Generalizations article and sent it to Armenian Journal of Mathematics for peer review. The main change in this version is a counter-example to the conjecture, that every weak partition of a filter object…

read more