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PFA and guessing models

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Abstract

This paper explores the consistency strength of The Proper Forcing Axiom (PFA) and the theory (T) which involves a variation of the Viale–Weiβ guessing hull principle. We show that (T) is consistent relative to a supercompact cardinal. The main result of the paper is Theorem 0.2, which implies that the theory “ADR + ⊝ is regular” is consistent relative to (T) and to PFA. This improves significantly the previous known best lower-bound for consistency strength for (T) and PFA, which is roughly “ADR + DC”.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92717, USA

    Nam Trang

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  1. Nam Trang
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Correspondence to Nam Trang.

Additional information

This work is partially supported by NSF grant DMS-1565808.

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Trang, N. PFA and guessing models. Isr. J. Math. 215, 607–667 (2016). https://doi.org/10.1007/s11856-016-1390-x

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  • DOI: https://doi.org/10.1007/s11856-016-1390-x

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