April 17, 2007
Abstract: It is a result from Martin that ultrapowers on strong partition cardinals are cardinals. The Axiom of Determinacy gives us strong partition cardinals. So in this context we can talk about measure analysis, i.e., whether it is possible to describe cardinals as ultrapowers in a canonical way. So we want an assignment of measures to cardinals and vice versa that has the right properties.
In my talk I will give an overview of the apparatus neccessary for this task. The construction of the actual measure assignment is by induction, since the measures needed to analyse a cardinal are built from measures on cardinals below it.
I will present the first step of this inductive analysis of cardinals in more detail. And last but not least there are some nice applications that arise from the measure analysis.