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.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

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.