Uniformizing ladder system colorings and the rectangle refining property
Author:
Teruyuki Yorioka
Journal:
Proc. Amer. Math. Soc. 138 (2010), 29612971
MSC (2010):
Primary 03E50, 03E05, 03E35
Published electronically:
March 17, 2010
MathSciNet review:
2644907
Fulltext PDF Free Access
Abstract 
References 
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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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 K. Devlin and S. Shelah. A weak version of which follows from . Israel J. Math. 29 (1978), no. 23, 239247. MR 0469756 (57:9537)
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 P. Eklof and S. Shelah. A combinatorial principle equivalent to the existence of nonfree Whitehead groups. Abelian Group Theory and Related Topics (Oberwolfach, 1993), 7998, Contemp. Math., 171, Amer. Math. Soc., Providence, RI, 1994. MR 1293134 (95g:20056)
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 5.
 P. Larson and F. Tall. Locally compact perfectly normal spaces may all be paracompact, preprint.
 6.
 P. Larson and S. Todorčević. Chain conditions in maximal models. Fund. Math. 168 (2001), no. 1, 77104. MR 1835483 (2002e:03067)
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 P. Larson and S. Todorčević. Katětov's problem. Trans. Amer. Math. Soc. 354 (2002), no. 5, 17831791. MR 1881016 (2003b:54033)
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 T. Miyamoto. Souslin trees under countable support iterations. Fund. Math. 142 (1993), no. 3, 257261. MR 1220552 (94f:03060)
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 S. Todorčević. Partition Problems in Topology. Contemp. Math., 84, Amer. Math. Soc., Providence, Rhode Island, 1989. MR 980949 (90d:04001)
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 S. Todorčević. Chain conditions in topology. II, in preparation.
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 S. Todorčević and B. Veličković. Martin's axiom and partitions. Compositio Math. 63 (1987), no. 3, 391408. MR 909386 (89a:03094)
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 T. Yorioka. Some weak fragments of Martin's axiom related to the rectangle refining property. Arch. Math. Logic 47 (2008), no. 1, 7990. MR 2410821 (2009e:03097)
 13.
 T. Yorioka. The inequality can be considered as an analogue of Suslin's Hypothesis. Axiomatic Set Theory and SetTheoretic Topology (Kyoto 2007), Sūrikaisekikenkyūsho Kōkyūroku No. 1595 (2008), 8488.
 14.
 T. Yorioka. Rudin's Dowker space in the extension with a Suslin tree. Fund. Math. 201 (2008), no. 1, 5389. MR 2439023 (2009h:03067)
 15.
 T. Yorioka. A nonimplication between fragments of Martin's Axiom related to a property which comes from Aronszajn trees, Ann. Pure Appl. Logic 161 (2010), no. 4, 469487.
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Additional Information
Teruyuki Yorioka
Affiliation:
Department of Mathematics, Shizuoka University, Ohya 836, Shizuoka, 4228529, Japan
Email:
styorio@ipc.shizuoka.ac.jp
DOI:
http://dx.doi.org/10.1090/S000299391010330X
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 GrantinAid 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.
