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Forcing axioms, approachability, and stationary set reflection

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arxiv 1807.06129 v3 pith:GQEIXUTP submitted 2018-07-16 math.LO

Sean D. Cox This is my paper · ORCID
classification math.LO
keywords approachabilityaxiomsforcingprovereflectionsomestationarykrueger
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We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot be reversed; strengthen and simplify some results of Krueger about forcing axioms and approachability; and prove that some other related results of Krueger are sharp. We also adapt some ideas of Woodin to simplify and unify many arguments in the literature involving preservation of forcing axioms.

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  1. Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topics

    math.LO 2019-08 accept novelty 4.0 of 10

    A compact survey of strong Chang's Conjecture variants, their forcing and reflection equivalences, a new result on sealing forcings, and a list of open problems.

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