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Weak diamond and open colorings
Journal of Mathematical Logic 3 (01):119-125 (2003)
Abstract
The purpose of this article is to prove the relative consistency of certain statements about open colorings with 2ℵ0 < 2ℵ1. In particular both OCA and the statement that every 1–1 function of size ℵ1 is σ-monotonic are consistent with 2ℵ0 < 2ℵ1. As a corollary we have that 2ℵ0 < 2ℵ1 does not admit a ℙ max variation.Links
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References found in this work
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal.W. Hugh Woodin - 2002 - Bulletin of Symbolic Logic 8 (1):91-93.
On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ 1 -Dense Real Order Types.J. Steprans, Uri Abraham, Matatyahu Rubin & Saharon Shelah - 2002 - Bulletin of Symbolic Logic 8 (2):303.
On the consistency of some partition theorems for continuous colorings, and the structure of ℵ1-dense real order types.Uri Abraham, Matatyahu Rubin & Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (2):123-206.
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