2008 seminar talk: Lower Bounds for consistency of two substructure properties at aleph_omega
Talk held by Philip Welch (University of Bristol) at the KGRC seminar on 2008-11-13.
We consider algebras A on aleph_omega, and look at possible mutual stationarity properties they may enjoy. ("Mutual stationarity" is a concept introduced by Foreman and Magidor in their discussion of the, generally, non-saturatedness of the non-stationary ideal.) We look to see whether a sequence of sets S_n each stationary below aleph_n+1 can be "simultaneously stationary" as a sequence for all algebras A.
A second (but simpler for us) problem concerns a property and question of Pereira related to free subsets, internally approachable models, and the PCF conjecture.
Covering Lemma arguments using inner models provide lower bounds for both properties.