P-ideal dichotomy and weak squares

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 2013 English Publisher:Cambridge University Press (CUP)Journal:The Journal of Symbolic Logic, volume 78, pages 157-167 (issn: 0022-4812, eissn: 1943-5886,

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Authors: Raghavan, Dilip;

doi: 10.2178/jsl.7801100

P-ideal dichotomy and weak squares

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Abstract

AbstractWe answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes □κ,ωfor any uncountableκ. We also show that the P-ideal dichotomy implies the failure of □κ,<bprovided that cf(κ) >ω1.

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Keywords

Other set-theoretic hypotheses and axioms, P-ideal dichotomy, Consistency and independence results, weak square principle, Other combinatorial set theory, Cardinal characteristics of the continuum, 03E35, 03E65, 03E17, 03E05, Aronszajn tree

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