Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 20 August 2014, 17:00 hrs
Room: S17#04-04, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: On embedding certain partial orders into the P-points under Tukey
and RK reducibility.
The study of the global structure of the P-points was initiated
mainly by Blass in 1970s. In a paper in 1973 he asked what partially
ordered sets can be embedded into the P-points under the ordering of
Rudin-Keisler reducibility. This question is of most interest under some
hypothesis that guarantees the existence of many P-points, such as Martin’s
axiom for sigma-centered posets. In the 1973 paper he showed under this
assumption that both omega_1 and the reals can be embedded. This
result was later generalized to the coarser notion Tukey reducibility.
We will prove that under Martin’s axiom for sigma-centered posets
P(omega)/FIN can be embedded into the P-points both under Rudin-Keisler
and Tukey reducibilities. Since P(omega)/FIN is universal for partial
orders of size at most continuum, this a good step towards giving a
complete answer to Blass’ original question.
This is joint work with Saharon Shelah.