Sh:1058

• Raghavan, D., & Shelah, S. (2017). On embedding certain partial orders into the P-points under Rudin-Keisler and Tukey reducibility. Trans. Amer. Math. Soc., 369(6), 4433–4455. arXiv: 1411.0084 DOI: 10.1090/tran/6943 MR: 3624416
• Abstract:
  The study of the global structure of ultrafilters on the natural numbers with respect to the quasi-orders of Rudin-Keisler and Rudin-Blass reducibility was initiated in the 1970s by Blass, Keisler, Kunen, and Rudin. In a 1973 paper Blass studied the special class of P-points under the quasi-ordering of Rudin-Keisler reducibility. He asked what partially ordered sets can be embedded into the P-points when the P-points are equipped with this ordering. 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 his 1973 paper he showed under this assumption that both {\omega}_{1} and the reals can be embedded. This result was later repeated for the coarser notion of Tukey reducibility. We prove in this paper that Martin’s axiom for \sigma-centered posets implies that every partial order of size at most continuum can be embedded into the P-points both under Rudin-Keisler and Tukey reducibility.
• published version (23p)

@article{Sh:1058,
 author = {Raghavan, Dilip and Shelah, Saharon},
 title = {{On embedding certain partial orders into the P-points under Rudin-Keisler and Tukey reducibility}},
 journal = {Trans. Amer. Math. Soc.},
 fjournal = {Transactions of the American Mathematical Society},
 volume = {369},
 number = {6},
 year = {2017},
 pages = {4433--4455},
 issn = {0002-9947},
 mrnumber = {3624416},
 mrclass = {03E50 (03E05 03E35 06E05 54D80)},
 doi = {10.1090/tran/6943},
 note = {\href{https://arxiv.org/abs/1411.0084}{arXiv: 1411.0084}},
 arxiv_number = {1411.0084}
}