P-ideal dichotomy and weak squares

Journal of Symbolic Logic 78 (1):157-167 (2013)

Abstract
We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$
Keywords P-ideal dichotomy   weak square principle   Aronszajn tree
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DOI 10.2178/jsl.7801100
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Set Mapping Reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
Combinatorial Dichotomies in Set Theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.

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