We investigate how much information cardinal invariants can give on the
structure of the ordered set on which they are de�ned. We consider the basic
de�nitions of an ordered set and see how they are related to one another.
We generalize some results on cardinal invariants for ordered sets and state
some useful characterizations. We investigate how cardinal invariants can
in
uence the existence of some special suborderings. We generalize some
results on the Dilworth and Sierpinski theorems and explore the conjecture
of Miller and Sauer. We address some open problems on dominating numbers.
We investigate Model Games to �nd some characterizations on the
cardinality of a set.
