Diego A. Mejía: Separating the left side of Cichon’s diagram

Friday Set Theory Seminar (HUJI)

We shall meet this Friday (May 8th) in the Hebrew University
math department building in Room 110, at 10 am.

Speaker: Diego A. Mejía (TU WIEN)

Title: Separating the left side of Cichon’s diagram

Abstract: It is well known that, with finite support iterations of ccc posets, we can obtain models where 3 or more cardinals of Cichon’s diagram can be separated. For example, concerning the left side of Cichon’s diagarm, it is consistent that \aleph_1 < add(N) < cov(N) < b < non(M)=cov(M)=c. Nevertheless, getting the additional strict inequality non(M) < cov(M) is a challenge because subposets of E, the standard ccc poset that adds an eventually different real, may add dominating reals (by Pawlikowski, 1992).

We construct a model of \aleph_1 < add(N) < cov(N) < b < non(M) < cov(M)=c with the help of chains of ultrafilters that allows to preserve certain unbounded families. This is a joint work with M. Goldstern and S. Shelah.

See you there!

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