Some more on measurable cardinals | Department of Mathematics

Some more on measurable cardinals

Event Information
Event Location: 
GAB 461
Event Date: 
Wednesday, October 16, 2013 - 3:30pm

We will review the construction of an ultrapower embedding from V into an inner model using a measurable cardinal κ and show that κ is the critical point of this embedding. Conversely, we will show that every nontrivial embedding has a critical point and sketch the argument that this critical point is measurable. Finally, we will use a normal measure on such a κ to prove that measurable cardinals are Ramsey in the very strong sense that the homogeneous set is not only of large cardinality but is large with respect to the measure.