Indestructible guessing models and the continuum

Sean Cox ¹   ; John Krueger ²

¹ Department of Mathematics and Applied Mathematics Virginia Commonwealth University 1015 Floyd Avenue P.O. Box 842014 Richmond, VA 23284, U.S.A.
² Department of Mathematics University of North Texas 1155 Union Circle #311430 Denton, TX 76203, U.S.A.

Fundamenta Mathematicae, Tome 239 (2017) no. 3, pp. 221-258

Résumé

We introduce a stronger version of an $\omega _1$-guessing model, which we call an indestructibly $\omega _1$-guessing model. The principle $\mathsf {IGMP}$ states that there are stationarily many indestructibly $\omega _1$-guessing models. This principle, which follows from $\mathsf {PFA}$, captures many of the consequences of $\mathsf {PFA}$, including the Suslin hypothesis and the singular cardinal hypothesis. We prove that $\mathsf {IGMP}$ is consistent with the continuum being arbitrarily large.

Détail

DOI : 10.4064/fm340-1-2017

Keywords: introduce stronger version omega guessing model which call indestructibly omega guessing model principle mathsf igmp states there stationarily many indestructibly omega guessing models principle which follows mathsf pfa captures many consequences mathsf pfa including suslin hypothesis singular cardinal hypothesis prove mathsf igmp consistent continuum being arbitrarily large