We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection

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Annals of Pure and Applied Logic 161 (1):94-108 (2010)
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Abstract

We present several forcing posets for adding a non-reflecting stationary subset of Pω1, where λ≥ω2. We prove that PFA is consistent with dense non-reflection in Pω1, which means that every stationary subset of Pω1 contains a stationary subset which does not reflect to any set of size 1. If λ is singular with countable cofinality, then dense non-reflection in Pω1 follows from the existence of squares

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2009

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10.1016/j.apal.2009.06.002

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David Aspero
University of East Anglia

Citations of this work

Forcing axioms, approachability, and stationary set reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.
Operations, climbability and the proper forcing axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.

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References found in this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, squares and reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
Combinatorial principles in the core model for one Woodin cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Shelah's pcf theory and its applications.Maxim R. Burke & Menachem Magidor - 1990 - Annals of Pure and Applied Logic 50 (3):207-254.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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