Forcing axioms, approachability, and stationary set reflection

Journal of Symbolic Logic 86 (2):499-530 (2021)
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Abstract

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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10.1017/jsl.2020.4

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References found in this work

Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Guessing models and generalized Laver diamond.Matteo Viale - 2012 - Annals of Pure and Applied Logic 163 (11):1660-1678.
Fragments of Martin's Maximum in generic extensions.Y. Yoshinobu & B. Konig - 2004 - Mathematical Logic Quarterly 50 (3):297.
PFA and Ideals on $\omega_{2}$ Whose Associated Forcings Are Proper.Sean Cox - 2012 - Notre Dame Journal of Formal Logic 53 (3):397-412.

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