2016/08/19 by Trang, Nam
#03E45 #03E47 #03E55 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1608.05726
This paper explores the consistency strength of The Proper Forcing Axiom (\textsfPFA) and the theory (T) which involves a variation of the Viale-Weiß guessing hull principle. We show that (T) is consistent relative to a supercompact cardinal. The main result of the paper implies that the theory "\sfAD_ℝ + Θ is regular" is consistent relative to (T) and to \textsfPFA. This improves significantly the previous known best lower-bound for consistency strength for (T) and \textsfPFA, which is roughly "\sfAD_ℝ + \textsfDC".