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!