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

 

Directive trees and games on posets


Authors: Tetsuya Ishiu and Yasuo Yoshinobu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1477-1485
MSC (2000): Primary 03E40; Secondary 03E65
Published electronically: October 12, 2001
MathSciNet review: 1879973
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Abstract: We show that for any infinite cardinal $\kappa $, every $(\kappa +1)$-strategically closed poset is $\kappa ^{+}$-strategically closed if and only if $\square _{\kappa }$ holds. This extends previous results of Velleman, et.al.


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Additional Information

Tetsuya Ishiu
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: tishiu@math.uci.edu

Yasuo Yoshinobu
Affiliation: Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan
Email: yosinobu@math.nagoya-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06235-9
PII: S 0002-9939(01)06235-9
Keywords: Directive trees, strategic closure
Received by editor(s): November 2, 2000
Published electronically: October 12, 2001
Additional Notes: The second author was partially supported by Grant-in-Aid for Scientific Research (No.11640112), Ministry of Education, Science and Culture, Japan
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2001 American Mathematical Society