Monroe Eskew: The Structure of Ideals

Monday, March 05, 2012, at 4pm
RH 440R

Speaker: Monroe Eskew (UCI)

Title: The Structure of Ideals

Abstract:

We present a proof of a theorem of Gitik and Shelah that places limits on the structure of quotient algebras by sigma-additive ideals. We will start
by showing connections between Cohen forcing and Baire category on the reals. Then by using generic ultrapowers, we will prove that no sigma-additive ideal yields an atomless algebra with a countable dense subset. We will discuss connections with Ulam’s measure problem: How many measures does it take to measure all sets of reals?

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.