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March 2013 P-ideal dichotomy and weak squares
Dilip Raghavan
J. Symbolic Logic 78(1): 157-167 (March 2013). DOI: 10.2178/jsl.7801100

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 $cf(\kappa) > {\omega}_{1}$.

Citation

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Dilip Raghavan. "P-ideal dichotomy and weak squares." J. Symbolic Logic 78 (1) 157 - 167, March 2013. https://doi.org/10.2178/jsl.7801100

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1323.03061
MathSciNet: MR3087067
Digital Object Identifier: 10.2178/jsl.7801100

Subjects:
Primary: 03E35, 03E65, 03E17, 03E05

Keywords: Aronszajn tree , P-ideal dichotomy , weak square principle

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 1 • March 2013
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