Japanese here
TAKAHASHI Makoto, Sc.D.
Division of Mathematics and Informatics
Department of Science of Human Environment
Faculty of Human Development
Kobe University
TSURUKABUTO 3-11, NADA,KOBE
JAPAN
E-mail:

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List of Research Contributions
Refereed Journal Publications
  1. $\sigma$-Short Boolean Algebras
    Mathematical Logic Quarterly Vol. 49 No. 6 (2003), pp543-549;MR2013715 (2004h:03132)
    (with Y.Yoshinobu)
  2. On extended Banach-Mazur games on Boolean algebras
    Scienticae Mathematicae Vol. 1 No. 2 (1998), pp169-176;MR1686224 (2000g:06010)
  3. On $L_{\infty\kappa}$-free Boolean algebras
    Annals of Pure and applied Logic Vol. 55 (1992), pp265-284 ;MR1153513 (93i:03053)
    (with S. Fuchino and S. Koppelberg)
  4. Completeness of Boolean Powers of Boolean Algebras
    Journal of the Mathematical Society of Japan Vol. 40 (1988), pp445-456;MR0945346 (89i:06023)
  5. The System FLm,n for specification analysis and the completeness theorem
    Journal of Information Processing, Vol. 9 (1986), pp220-227
    (with K. Hirose and S.Yamada)
  6. The System FLm,n for specification analysis and an automatic theorem prover for FLm,n
    Bulletin of Centre for Informatics Waseda University Vol. 3 (1986), pp51-58
    (with K. Hirose and S.Yamada)
  7. Iterated Boolean Powers
    Comment. Math. Univ. St. Pauli, Vol. 34 (1985), pp59-58;MR0789513 (86j:03030)
  8. A formal system for specification Analysis of Concurrent Programs
    Publ. of the R.I.M.S. Kyoto University Vol. 19 (1983), pp911-926
    (with K. Hirose);MR0723455 (86g:68050)
  9. Topological Powers and Reduced Powers
    Tokyo Journal of Mathematics Vol. 3 (1980) ,pp141-147;MR0584552 (82c:03040)
Other Papers, Proceedings
  1. On non $\sigma$-shortness of Axiom A posets with frame systems, Kyoto daigaku surikaiseki kenkyusho kokyuroku 1988(2016), pp.65-76
  2. Some characterizations of strongly \sigma-short Boolean Algebras
    Kyoto daigaku surikaiseki kenkyusho kokyuroku 1423 (2005),pp.124-127
  3. On Strongly \sigma-short Boolean algebras
    Proceedings of General Topology Symposium held in Kobe, 2002, pp 74-79
  4. On uncountable representability of cBa under \neg CH (Japanese),
    Kyoto daigaku surikaiseki kenkyusho kokyuroku 930 (1995),pp.1-9
  5. On Potentially Free Boolean Algebras
    Proceedings of The Fourth Asian Logic Conference,1990, p147
Preprint
  1. Axiom A trees are essentially ccc or \sigma-closed

On non $\sigma$-shortness of Axiom A posets with frame systems

Kyoto daigaku surikaiseki kenkyusho kokyuroku 1988(2016), pp.65-76 pdf

We show that Axiom A posets with frame systems are not $\sigma$-short.

Some characterizations of strongly \sigma-short Boolean Algebras

Kyoto daigaku surikaiseki kenkyusho kokyuroku 1423 (2005),pp.124-127

We give some characterizations of strongly \sigma-short Boolean algebras.

On 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.

\sigma-Short Boolean Algebras

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.

On extended Banach-Mazur games on 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.

On L_{\infty\kappa}-free Boolean algebras

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.