2013 Fiscal Year Final Research Report
On reflection principles at small uncountable cardinals
| Project/Area Number |
23740076
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
SAKAI Hiroshi 神戸大学, システム情報学研究科, 准教授 (70468239)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 公理的集合論 / 反映原理 / 巨大基数公理 / 無限組み合わせ論 |
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| Research Abstract |
I investigated reflection principles at small uncountable cardinals, in particular, their consistencies and their relationships with infinite combinatorics, forcing axioms and large cardinal axioms. Among other things, the following results were obtained: (1) I clarified how weak square principles are denied by each reflection principle at omega 2. (2) By showing that the forcing axiom MA+ (sigma-closed) does not follow from any variation of stationary reflection principles at omega 2, I clarified the difference between reflection principles and forcing axioms. (3) It was proved that in L there is a correspondence between hierarchies of stationary reflection principles and indescribable cardinals.
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