A correction to “A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees”

In the paper A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees (Yorioka, 2010 [1]), Proposition 2.7 is not true. To avoid this error and correct Proposition 2.7, the definition of the property R 1 , ℵ 1 is changed. In Yorioka (2010) [1], all proofs of lemmas and theorems but Lemma 6.9 are valid about this definition without changing the proofs. We give a new statement and a new proof of Lemma 6.9.