Directive trees and games on posets

Tetsuya Ishiu, Yasuo Yoshinobu
2001 Proceedings of the American Mathematical Society  
We show that for any infinite cardinal κ, every (κ+1)-strategically closed poset is κ + -strategically closed if and only if κ holds. This extends previous results of Velleman, et.al.
doi:10.1090/s0002-9939-01-06235-9 fatcat:hihcxzmusfax3iwm5bzteejwoq