Ultrafilters (with Dense Elements) over Closure Spaces

Ultrafilters (with Dense Elements) over Closure Space

Combinatorial criteria for ramifiable ordered sets

The tree-property (classical in cardinal theory) and its variants make sense also for directed sets and even for partially ordered sets. A combinatorial approach is developed here, with characterizations and criteria involving (inter alia) adequate families of special substructures of directed sets. These substructures form a natural hierarchy that is also investigated.SCOPUS: ar.jFLWINinfo:eu-repo/semantics/publishe