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Some weak fragments of Martin’s axiom related to the rectangle refining property
Archive for Mathematical Logic 47 (1):79-90 (2008)
Abstract
We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragmentsLinks
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Citations of this work
Two chain conditions and their Todorčević's fragments of Martin's Axiom.Teruyuki Yorioka - 2024 - Annals of Pure and Applied Logic 175 (1):103320.
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Forcing the Mapping Reflection Principle by finite approximations.Tadatoshi Miyamoto & Teruyuki Yorioka - 2021 - Archive for Mathematical Logic 60 (6):737-748.
The relative strengths of fragments of Martin's axiom.Joan Bagaria - 2024 - Annals of Pure and Applied Logic 175 (1):103330.
References found in this work
On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ 1 -Dense Real Order Types.J. Steprans, Uri Abraham, Matatyahu Rubin & Saharon Shelah - 2002 - Bulletin of Symbolic Logic 8 (2):303.
On the consistency of some partition theorems for continuous colorings, and the structure of ℵ1-dense real order types.Uri Abraham, Matatyahu Rubin & Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (2):123-206.
Fragments of Martin's axiom and δ13 sets of reals.Joan Bagaria - 1994 - Annals of Pure and Applied Logic 69 (1):1-25.
The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap.Teruyuki Yorioka - 2005 - Archive for Mathematical Logic 44 (6):677-683.
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