Uniformizing ladder system colorings and the rectangle refining property

Yorioka, Teruyuki

doi:10.1090/S0002-9939-10-10330-X

Uniformizing ladder system colorings and the rectangle refining property
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Proc. Amer. Math. Soc. 138 (2010), 2961-2971 Request permission

Abstract:

We investigate forcing notions with the rectangle refining property, which is stronger than the countable chain condition, and fragments of Martin’s Axiom for such forcing notions. We prove that it is consistent that every forcing notion with the rectangle refining property has precaliber $\aleph _1$ but $\mathsf {MA}_{\aleph _1}$ for forcing notions with the rectangle refining property fails.

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