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:
Department of Science of Human Environment

Faculty of Human Development

Kobe University

TSURUKABUTO 3-11, NADA,KOBE

JAPAN

How to install RStudio Desktop/Server on Raspberry Pi 2 or 3(Summary)

List of Research Contributions

Refereed Journal Publications

- $\sigma$-Short Boolean Algebras

Mathematical Logic Quarterly Vol. 49 No. 6 (2003), pp543-549;MR2013715 (2004h:03132)

(with Y.Yoshinobu) - On extended Banach-Mazur games on Boolean algebras

Scienticae Mathematicae Vol. 1 No. 2 (1998), pp169-176;MR1686224 (2000g:06010)

- 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) - Completeness of Boolean Powers of Boolean Algebras

Journal of the Mathematical Society of Japan Vol. 40 (1988), pp445-456;MR0945346 (89i:06023) - The System FL
_{m,n}for specification analysis and the completeness theorem

Journal of Information Processing, Vol. 9 (1986), pp220-227

(with K. Hirose and S.Yamada) - The System FL
_{m,n}for specification analysis and an automatic theorem prover for FL_{m,n}

Bulletin of Centre for Informatics Waseda University Vol. 3 (1986), pp51-58

(with K. Hirose and S.Yamada) - Iterated Boolean Powers

Comment. Math. Univ. St. Pauli, Vol. 34 (1985), pp59-58;MR0789513 (86j:03030) - 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) - Topological Powers and Reduced Powers

Tokyo Journal of Mathematics Vol. 3 (1980) ,pp141-147;MR0584552 (82c:03040)

Other Papers, Proceedings

- On non $\sigma$-shortness of Axiom A posets with frame systems, Kyoto daigaku surikaiseki kenkyusho kokyuroku 1988(2016), pp.65-76
- Some characterizations of strongly \sigma-short Boolean Algebras

Kyoto daigaku surikaiseki kenkyusho kokyuroku 1423 (2005),pp.124-127 - On Strongly \sigma-short Boolean algebras

Proceedings of General Topology Symposium held in Kobe, 2002, pp 74-79 - On uncountable representability of cBa under \neg CH (Japanese),

Kyoto daigaku surikaiseki kenkyusho kokyuroku 930 (1995),pp.1-9 - On Potentially Free Boolean Algebras

Proceedings of The Fourth Asian Logic Conference,1990, p147

- Axiom A trees are essentially ccc or \sigma-closed

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

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

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.