Combinatorial Criteria for Ramifiable Ordered Sets
Olivier Esser, Roland Hinnion · Mathematical logic quarterly · 2001
The tree-property (classica in cardina theory) and its variants make sense also for directed sets and even for partially ordered sets. A combinatoria 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.