| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
We characterized the existence of weakly compact cardinals in terms of iterations of weakly Mahlo operations. We described ZF-provably existing countable ordinals by means of iterations of Mostowski collapsings. We introduced a class of set functions, which are computable in polynomial time, and introduced a theory in which $\Sigma_{1}$-definable functions are exactly polynomial time computable set functions. We showed that intuitionistic fixed point theories over a weak set theory is a conservative extension of the weak set theory. We showed that the wellordering principle of the derivative of a normal function on ordinals is equivalent to the existence of arbitrarily large countable coded $\omega$-models of the normal function. We gave a finitary procedure by which cut inferences are eliminated from derivations for set theory of $\omega_{1}$. We determined a line between predicative and impredicative fragments of the theory of positive elementary inductive definitions.
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