Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-01-06235-9
Published electronically: October 12, 2001
MathSciNet review: 1879973
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [F] M. Foreman, Games played on boolean algebras, J. of Symbolic Logic 48 (1983), 714-723. MR 85h:03064
  • [G] C. Gray, Iterated forcing from the strategic point of view, Ph.D. Thesis, University of California, Berkeley, 1980.
  • [I] T. Ishiu, On Axiom A and games on boolean algebras (Japanese), Master Thesis, Waseda University, 1997.
  • [J1] T. Jech, A game theoretic property of Boolean algebras, Logic Colloquium '77 (A. Macintyre, L. Pacholski and J. Paris, eds.), North-Holland, Amsterdam, 1978, pp. 135-144. MR 80c:90184
  • [J2] T. Jech, More game-theoretic properties of Boolean algebras, Ann. Pure Appl. Logic 26 (1984), 11-29. MR 85j:03110
  • [Vc] B. Velickovic, Jensen's $\square $ principles and the Novák number of partially ordered sets, J. of Symbolic Logic 51 (1986), 47-58. MR 87h:03074
  • [Vm] D. Velleman, On a generalization of Jensen's $\square _{\kappa }$, and strategic closure of partial orders, J. of Symbolic Logic 48 (1983), 1046-1052. MR 85g:03076

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E40, 03E65

Retrieve articles in all journals with MSC (2000): 03E40, 03E65


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: https://doi.org/10.1090/S0002-9939-01-06235-9
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

American Mathematical Society