Weak square bracket relations for P κ (λ)

Journal of Symbolic Logic 73 (3):729-751 (2008)
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Abstract

We study the partition relation $X@>{\rm w}>>[Y]_{p}^{2}$ that is a weakening of the usual partition relation $X\rightarrow [Y]_{p}^{2}$ . Our main result asserts that if κ is an uncountable strongly compact cardinal and $\germ{d}_{\kappa}\leq \lambda ^{<\kappa}$ , then $I_{\kappa,\lambda}^{+}@>{\rm w}>>[I_{\kappa,\lambda}^{+}]_{\lambda <\kappa}^{2}$ does not hold

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Piece selection and cardinal arithmetic.Pierre Matet - 2022 - Mathematical Logic Quarterly 68 (4):416-446.

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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.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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