Mathematical Sciences: Foundation of Mathematics and its Applications

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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.