Kyoto daigaku surikaiseki kenkyusho kokyuroku 1423 (2005),pp.124-127
We give some characterizations of strongly \sigma-short Boolean algebras.
Proceedings of General Topology Symposium held in Kobe, 2002, pp.74-79
We investigate strongly \sigma-shortness of some Boolean algebras. Especially, we show that every (\kappa, \omega)-caliber Boolean algebra of density \geq \kappa is not strongly \sigma-short.
Mathematical Logic Quarterly Vol. 49 No. 6 (2003), pp543-549;MR2013715 (2004h:03132)
(with Y.Yoshinobu)
We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach-Mazur Boolean game. A \sigma-short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length \omega does not have a nonzero lower bound. We give a characterization of $\sigma$-short Boolean algebras and study properties of \sigma-short Boolean algebras.
Scienticae Mathematicae Vol. 1 No. 2 (1998), pp169-176
We extend the Banach-Mazur game on Boolean algebras so that at each stage player I can play simultaneously many elements. We introduce two games S(B) and D(B) . We show that S(B) is determined for all Boolean algebras and D(B) is determined for several Boolean algebras for which ordinary Banach-Mazur game is undetermined.
Annals of Pure and applied Logic Vol. 55 (1992), pp265-284
(with S. Fuchino and S. Koppelberg)
We study L_{\infty\kappa}-freeness in the variety of Boolean algebras. It is shown that some of the theorem on L_{\infty\kappa}-free algebras which are known to hold in varietie such as groups, abelian groups etc. are also true for Boolean algebras. But we also investigate properties such as the ccc of L_{\infty\omega_1}-free Boolean algebras which have no counterpart in the varieties above.