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

DOI:
https://doi.org/10.1090/S0002-9939-10-10330-X

Published electronically:
March 17, 2010

MathSciNet review:
2644907

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Abstract | References | Similar Articles | Additional Information

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 but 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:
https://doi.org/10.1090/S0002-9939-10-10330-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.