Partially Ordered Sets and Their Invariants
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. 2
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