# 30/Nov/12: Christina Brech and Alan Dow

30/November/2012, 11:o0–12:00
Fields institute,Room 230

Speaker: Chtistina Brech

Title: The Banach space $\ell_\infty/c_0$ in the Cohen model

Abstract: We will present some results concerning nonexistence of isomorphic copies of certain Banach spaces inside $\ell_\infty/c_0$ in the Cohen model. As opposed to results obtained under CH, we conclude that in the Cohen model the space $\ell_\infty/c_0$ cannot contain a copy of all Banach spaces of density continuum and cannot be written as an $\ell_\infty$-sum of any given Banach space X.
These are joint results with Piotr Koszmider.

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30/November/2012, 13:30–15:00
Fields institute,Room 230

Speaker: Alan Dow

Title: Non-trivial copies of N* in N*

Abstract: It is a rather old problem of E. van Douwen to determine if there is (in ZFC) a non-trivial copy of N* in N*. It is folklore that for any countable discrete subset D of N*, the subspace consisting of the limit points of D is itself a copy of N*. These are known as the trivial copies of N*. CH implies there are many non-trivial copies of N* but, following Shelah’s work in on the consistency of the non-existence of autohomeomorphisms of N*, negative partial results were obtained by W. Just and I. Farah. In particular, it follows from the PFA that the dual ideal generated by any possible non-trivial copy of N* would have to satisfy the ccc over fin property (Farah).