Mathematical logic and order theory

An inescapable conclusion of the study of order theory is that mathematical logic is deeply intertwined with the study of partial ordering relations. We can form partial orders called concept hierarchies corresponding to the logical inclusion of predicates and we can represent elements of partial orders that form distributive lattices including well orders as sets or predicates. This naturally leads to the definition of Von Neumann ordinals in a well order for example. A description of the relation between mathematical logic and order theory is forthcoming.