| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
There are several open problems on Ramsey theoretic properties and assertions. For example, the countable chain condition is a representative of Ramsey theoretic properties on the forcing theory, and the following assertions can be considered as Ramsey theoretic assertions: There are no S-spaces, there are no entangled sets of reals, and the P-ideal Dichotomy.
In the project, it is studied that (1) Prikry's problem on ccc forcings, (2) new properties of ideal-based forcings, and (3) the consistency about the existence of a non-special Aronszajn tree with a couple of Ramsey theoretic assertions.
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