Monroe Eskew: The structure of ideals II

Monday, March 12, 2012, at 4pm
RH 440R

Speaker: Monroe Eskew (UCI)

Title: The structure of ideals II


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?

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