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FORCING AXIOMS, APPROACHABILITY, AND STATIONARY SET REFLECTION

Part of: Set theory

Published online by Cambridge University Press:  20 October 2021

SEAN D. COX
SEAN D. COX*
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VIRGINIA COMMONWEALTH UNIVERSITY 1015 FLOYD AVENUE, RICHMOND, VA23284, USAE-mail: [email protected]
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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.

Keywords

forcing axiomsapproachabilityinternally approachableMartin’s Maximum

MSC classification

Primary: 03E55: Large cardinals
Secondary: 03E35: Consistency and independence results
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 2 , June 2021 , pp. 499 - 530
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Copyright
© The Association for Symbolic Logic 2021

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