Internal approachability and reflection

Journal of Mathematical Logic 8 (1):23-39 (2008)

Abstract

We prove that the Weak Reflection Principle does not imply that every stationary set reflects to an internally approachable set. We show that several variants of internal approachability, namely, internally unbounded, internally stationary, and internally club, are not provably equivalent.

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References found in this work

Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.

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Citations of this work

Guessing Models and Generalized Laver Diamond.Matteo Viale - 2012 - Annals of Pure and Applied Logic 163 (11):1660-1678.
Some Applications of Mixed Support Iterations.John Krueger - 2009 - Annals of Pure and Applied Logic 158 (1-2):40-57.
Forcing Axioms, Approachability, and Stationary Set Reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.

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