Speaker: Benjamin Claverie, University of Muenster

Title: Changing u_2 by stationary set preserving forcing

Abstract: We show that if I is a precipitous ideal on
\omega_1 and \theta > \omega_1 is regular, then there is a
stationary set preserving forcing which adds a countable
structure (M,J) which iterates to (H_\theta,I) in \omega_1
steps. Therefore, if there is a precipitous ideal on
\omega_1 and the universe is closed under sharps, then there
is a stationary set preserving forcing which increases u_2.
If BMM holds and there is a precipitous ideal on \omega_1,
then u_2 = \omega_2.