Abstract

We replace Shelah's notion of true cofinality by the notion of the bounding number for an arbitrary partial order and begin to develop a theory similar to Shelah's pcf theory, which gives many analog results, including the existence of the so-called generators, for the more general case of products of partial orders. The development can be strictly divided into an ideal theoretical and a combinatorial part. We also show that pcf theory is a special case of this more general theory and conclude with some remarks about Shelah's function pp, which also show that there are some differences between pcf theory and the presented theory of bounding numbers