A Galvin-Hajnal theorem for generalized cardinal characteristics, part 1

We prove that a variety of generalized cardinal characteristics,  including meeting numbers, the reaping number, and the dominating number, satisfy an analogue of the Galvin-Hajnal theorem, and hence also of Silver's theorem, at singular cardinals of uncountable cofinality. In the first talk, we will introduce some fundamental PCF-theoretic facts due to Shelah and Jech that will be used in our proof, and in the second talk we will prove our generalized Galvin-Hajnal theorem.