Measurable Cardinals, or, How I learned to stop worrying about ultraproducts and love elementary embeddings

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.