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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Directive trees and games on posets
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by Tetsuya Ishiu and Yasuo Yoshinobu
Proc. Amer. Math. Soc. 130 (2002), 1477-1485
DOI: https://doi.org/10.1090/S0002-9939-01-06235-9
Published electronically: October 12, 2001
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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.
References
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Bibliographic 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
  • 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.
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1477-1485
  • MSC (2000): Primary 03E40; Secondary 03E65
  • DOI: https://doi.org/10.1090/S0002-9939-01-06235-9
  • MathSciNet review: 1879973