In this talk, I will give many of the basic definitions of PCF theory and prove some basic facts. I will define the objects pcf(A) and J_{<\lambda} among others. Then I will show how these objects are not only integral to PCF theory, but also to the universe of set theory.

Returning to the PCF theory proper, I will relate the discussion of the last couple of weeks to the proofs of many of the theorems of PCF theory. The goal of this talk is to give enough background in PCF theory to understand the statements of some of the harder theorems.

This talk will be a survey with a little set theory required. This talk is also mostly independent from the talks of the previous weeks.

The notes for the talk will be posted at my logic web page.