Since then, Shelah's pcf theory has justified these hopes to a great extent; along the way, it has changed the language of cardinal arithmetic by focusing attention on relatively concrete objects whose properties are often fixed by the ZFC axioms. In particular, it has proven fruitful to study the "pseudopower" function in place of the classical power function on singular cardinals.

The talk will introduce pseudopowers, survey some results and questions connected with them, and describe how methods from pcf theory can be used to extend Silver's theorem in several directions.