| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
We investigated the combinatorial structure of the continuum using novel techniques from forcing theory. In particular, we employed techniques like Mathias forcing with a filter and other ccc forcing notions, a sophisticated version of finite support iteration of forcing, matrix iterations of forcing, generalizations of forcing notions on the real numbers to large cardinals etc, to obtain new independence results about the order relationship between cardinal invariants of the continuum, and about sets of real numbers with maximality properties like ultrafilters and maximal almost disjoint families.
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