Using ideas from Foreman-Magidor-Shelah, one can force from a Wooden cardinal to show it is consistent that the nonstationary ideal on \(\omega_1\) is saturated while the quotient boolean algebra is rigid. The key is to apply Martin's Axiom to the almost-disjoint coding forcing to see how it interacts with a generic elementary embedding. This strategy requires the continuum hypothesis to fail. Towards showing the consistency of rigid ideals with GCH, the speaker investigated other coding strategies: stationary coding (with Brent Cody), a rigid version of the Levy collapse, and ladder-system coding (in recent work with Paul Larson). We have some equiconsistencies about rigid ideals on \(\omega_1\) and \(\omega_2\), as well as some global possibilities from very large cardinals. Some natural questions remain about \(\omega_1\) and successors of singulars.
Rigid ideals
18.10.2018 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25