Mathematical Sciences: Foundation of Mathematics and its Applications

Gaisi Takeuti的研究分为两个项目：(1)有界算术证明理论和复杂性理论，(2)布尔值和heyting值模型。第一个与塞缪尔·巴斯（Samuel Buss）对竹井（Takeuti）在其《证明论》（Proof Theory）一书中最初提出的一个观点的概括有关。如果这能适用于复杂性理论所处理的多项式时间层次结构，那将是令人兴奋的。第二个项目涉及应用竹井首创的特殊模型方法来获得关于某些类型的群和概率度量空间的结果。

Gaisi Takeuti's research is divided into two projects: (1) proof theory of bounded arithmetic and complexity theory, (2) Boolean-valued and Heyting-valued models. The first is related to a generalization by Samuel Buss of an idea developed originally by Takeuti in his book on Proof Theory. It would be exciting if this could be adapted to work in the polynomial-time hierarchy that complexity theory treats. The second project involves applying the method of special models pioneered by Takeuti to obtain results about certain types of groups and probabilistic metric spaces.