2011 Fiscal Year Final Research Report
Reflection principles on stationarity and possible extensions of the axiom system of set thoery
| Project/Area Number |
21540150
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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 |
FUCHINO Sakae 神戸大学, システム情報学研究科, 教授 (30292098)
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| Research Collaborator |
LAJOS Soukup ハンガリー科学アカデミー, レニ数学研究所, 教授
FRIEDMAN Sy-david ウィーン大学, クルトーゲーデル研究センター, 教授
SAKAI Hiroshi 神戸大学, システム情報学研究科, 講師 (70468239)
USUBA Toshimichi 名古屋大学, 高等研究院, 特任助教 (10513632)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 数学基礎論 |
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| Research Abstract |
In this research project, we studied the so-called Fodor-type Reflection Principle(FRP) which is situated between stationarity reflection of sets of ordinals and that of sets of countable sets of ordinals. We proved that FRP is equivalent to many of the "mathematical" reflection principles which have been known as consequences of Fleissner's Axiom R. We also proved that FRP implies Shelah's Strong Hypothesis and obtained an almost complete picture of the implications and non implications among reflection principles including FRP.
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