Club-guessing, stationary reflection, and coloring theorems

Annals of Pure and Applied Logic 161 (10):1216-1243 (2010)
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Abstract

We obtain very strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. In particular, the simplest of our results establishes that if μ is singular and , then there is a regular cardinal θ<μ such that any fewer than cf stationary subsets of must reflect simultaneously

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10.1016/j.apal.2010.02.004

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Citations of this work

Chain conditions of products, and weakly compact cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
Getting more colors II.Todd Eisworth - 2013 - Journal of Symbolic Logic 78 (1):17-38.
Successors of Singular Cardinals and Coloring Theorems II.Todd Eisworth & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (4):1287 - 1309.
Getting more colors I.Todd Eisworth - 2013 - Journal of Symbolic Logic 78 (1):1-16.

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References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
A new class of order types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.

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