Series: Penn State Logic Seminar Date: Tuesday, October 14, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: Christopher Griffin, Penn State, Mathematics and ARL Title: Measurable Cardinals, or, How I learned to stop worrying about ultraproducts and love elementary embeddings Abstract: We will define what we mean by measurable cardinal and then sketch some consequences of the existence of measurable cardinals. In particular, we will show that every measurable cardinal is inaccessible and that if a measurable cardinal exists then V does not equal L. Interestingly enough, this is still not enough to settle the question of CH (We will not prove this). We will explore these consequences by way of ultraproducts of the universe over a well chosen complete ultrafilter. Other properties of measurable cardinals will be explored as time permits.