| Budget Amount *help |
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2019: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
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| Outline of Final Research Achievements |
The purpose of this study is to obtain multidimensional perspectives on the dynamism of "proof" by elucidating new incompleteness phenomena in the fundations of mathematics, e.g. the phase transition between provability and unprovability induced by parameters inserted in theorems, and supercritical propositions such as the determinacy of infinite games which cannot be proved by ordinary axioms.
During the first half of the plan, we proceeded the research in five sub-themes. In the latter half, we rearranged into the following three sub-themes and obtained remarkable results. (1) Reverse mathematics and non-standard methods. (2) Open game and Weihrauch degrees. (3) Query complexity of random decision trees.
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