The Galvin-Hajnal formula and its applications to Cardinal Arithmetic
The purpose of this talk is to present the main developments in Cardinal Arithmetic from 1960 to 1975. After a brief review of the basic independence results, we will review the basic definitions and results about ultrapowers and measurable cardinals and proceed to Scott's and Vopenka's results in Cardinal Arithmetic regarding measurable cardinals and singular cardinals of measurable cofinality. These results are generalizable to all singular cardinals of uncountable cofinality and this is what we will look at next. For that will start with the basic definitions and examples regarding the Galvin-Hajnal norm and finish with the application of the Galvin-Hajnal bound for families of almost disjoint functions to Cardinal Arithmetic.