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.
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{'Code': '1268', 'Text': 'FOUNDATIONS'}
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