Journal of Symbolic Logic

Approachability and games on posets

Yasuo Yoshinobu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We show that for any infinite cardinal κ, every strongly (κ+1)-strategically closed poset is strongly κ+-strategically closed if and only if APκ (the approachability property) holds, answering the question asked in [k5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 2 (2003), 589- 606.

Dates
First available in Project Euclid: 11 May 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1052669065

Digital Object Identifier
doi:10.2178/jsl/1052669065

Mathematical Reviews number (MathSciNet)
MR1976592

Zentralblatt MATH identifier
1055.03031

Citation

Yoshinobu, Yasuo. Approachability and games on posets. J. Symbolic Logic 68 (2003), no. 2, 589-- 606. doi:10.2178/jsl/1052669065. https://projecteuclid.org/euclid.jsl/1052669065


Export citation

References

  • J. Cummings, M. Foreman, and M. Magidor Squares, scales and stationary reflection, Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 35--98.
  • M. Foreman Games played on boolean algebras, Journal of Symbolic Logic, vol. 48 (1983), pp. 714--723.
  • M. Foreman and M. Magidor A very weak square principle, Journal of Symbolic Logic, vol. 62 (1997), no. 1, pp. 175--196.
  • T. Ishiu On Axiom A and games on boolean algebras, Master's thesis, Waseda University,1997, in Japanese.
  • T. Ishiu and Y. Yoshinobu Directive trees and games on posets, Proceedigs of the American Mathematical Society, to appear.
  • T. Jech A game theoretic property of Boolean algebras, Logic Colloquium '77 (A. Macintyre, L. Pacholski, and J. Paris, editors), North-Holland, Amsterdam,1978, pp. 135--144.
  • R. Jensen The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229--308.
  • W. Mitchell Aronszajn trees and independence of transfer property, Annals of Mathematical Logic, vol. 5 (1972), pp. 21--46.
  • S. Shelah On successors of singular cardinals, Logic Colloquium '78 (M. Boffa, D. van Dalen, and K. McAloon, editors), North-Holland, Amsterdam,1979, pp. 357--380.
  • B. Veli$\rm \Checkc$kovi$\rm \Checkc$ Jensen's $\square$ principles and the Novák number of partially ordered sets, Journal of Symbolic Logic, vol. 51 (1986), pp. 47--58.
  • D. Velleman On a generalization of Jensen's $\square_\kappa$, and strategic closure of partial orders, Journal of Symbolic Logic, vol. 48 (1983), pp. 1046--1052.