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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniformizing ladder system colorings and the rectangle refining property


Author: Teruyuki Yorioka
Journal: Proc. Amer. Math. Soc. 138 (2010), 2961-2971
MSC (2010): Primary 03E50, 03E05, 03E35
Published electronically: March 17, 2010
MathSciNet review: 2644907
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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 $ \operatorname{\sf {MA}}_{\aleph_1}$ for forcing notions with the rectangle refining property fails.


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Additional Information

Teruyuki Yorioka
Affiliation: Department of Mathematics, Shizuoka University, Ohya 836, Shizuoka, 422-8529, Japan
Email: styorio@ipc.shizuoka.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10330-X
PII: S 0002-9939(10)10330-X
Keywords: A uniformization of ladder system colorings, the rectangle refining property, fragments of Martin's Axiom
Received by editor(s): July 27, 2009
Received by editor(s) in revised form: December 6, 2009
Published electronically: March 17, 2010
Additional Notes: The author was supported by Grant-in-Aid for Young Scientists (B), No. 19740048, Ministry of Education, Culture, Sports, Science and Technology.
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.