PFA and guessing models

Nam Trang

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arXiv · 1608.05726

PFA and guessing models

Nam Trang

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Abstract

This paper explores the consistency strength of The Proper Forcing Axiom ($\textsf{PFA}$) and the theory (T) which involves a variation of the Viale-Wei$\ss$ guessing hull principle. We show that (T) is consistent relative to a supercompact cardinal. The main result of the paper implies that the theory "$\sf{AD}$$_\mathbb{R} + \Theta$ is regular" is consistent relative to (T) and to $\textsf{PFA}$. This improves significantly the previous known best lower-bound for consistency strength for (T) and $\textsf{PFA}$, which is roughly "$\sf{AD}$$_\mathbb{R} + \textsf{DC}$".

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Nam Trang. 2016-08-19. PFA and guessing models. https://arxiv.org/abs/1608.05726

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