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Good and bad points in scales
Archive for Mathematical Logic 53 (7):749-777 (2014)
Abstract
We address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik–Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the Gitik–Sharon model and other models containing bad scales. Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales.Other Versions
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Citations of this work
On the relationship between mutual and tight stationarity.William Chen-Mertens & Itay Neeman - 2021 - Annals of Pure and Applied Logic:102963.
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.
A very weak square principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
Canonical structure in the universe of set theory: Part two.James Cummings, Matthew Foreman & Menachem Magidor - 2006 - Annals of Pure and Applied Logic 142 (1):55-75.
Diagonal Prikry extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
The PCF Trichotomy Theorem does not hold for short sequences.Menachem Kojman & Saharon Shelah - 2000 - Archive for Mathematical Logic 39 (3):213-218.
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