PCF theory

This was the result which initiated Shelah's pcf theory.

In PCF theory the cardinal function is used.

The research on extending this result led Saharon Shelah to the invention of PCF theory.

PCF theory is the name of a mathematical theory, introduced by Saharon , that deals with the cofinality of the ultraproducts of ordered sets.

Using PCF theory, M. Kojman and S. Shelah constructed a subspace of Rudin's Dowker space of cardinality that is also Dowker.

With PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation.