# 28/Sep/2012: Michal Doucha, and Saharon Shelah

11:00–12:00
Bahen Centre, Room 2135

Speaker: Michal Doucha (Charles University)

Title:  Canonization of analytic equivalence relations for the Carlson-Simpson forcing

Absrtact:

I will present a forcing notion naturally associated to the Carlson-Simpson theorem. Since any condition of this forcing in fact corresponds to some closed set in $\mathcal{P}(\omega)$ we can talk about Borel or analytic equivalence relations defined on conditions. I will prove that for any condition and any analytic equivalence relation on it there is a subcondition on which this equivalence relation is just the identity or the full relation.

One of the consequences will be that for any analytic equivalence relation on $\mathcal{P}(\omega)$ there exists an infinite sequence $(A_i)_i$ of pairwise disjoint subsets of $\omega$ such that either for any two different arbitrary unions of such sets (both containing $A_0$ though) they are equivalent, or for any two different arbitrary unions both containing $A_0$ they are inequivalent.

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13:30–15:00
Fields institute,Room 230

Speaker: Saharon Shelah (HUJI & Rutgers)

Title:  Weak axiom of choice  :  can the dead be resurrected