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On reflection principles at small uncountable cardinals

On reflection principles at small uncountable cardinals
关于小不可数基数的反射原理
批准号:
23740076
负责人:
SAKAI Hiroshi
金额:
$2.16万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Young Scientists (B)
财政年份:
2011
资助国家:
日本
项目状态:
已结题
起止时间:
2011 至 2013

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英文摘要
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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期刊:
影响因子: --
作者: []
通讯作者:
On proofs of the incompleteness theorems based on Berry's paradox by Vopenka, Chaitin, and Boolos
Vopenka、Chaitin 和 Boolos 基于 Berry 悖论的不完备性定理的证明
DOI: --
发表时间: 2012
期刊: Mathematical Logic Quarterly
影响因子: 0.3
作者: [M. Kikuchi, T. Kurahashi and H. Sakai]
通讯作者: T. Kurahashi and H. Sakai
定常性反映原理と半定常性反映原理
平稳性反射原理和半平稳性反射原理
DOI: --
发表时间:
期刊:
影响因子: --
作者: [Takeshi Matsuda, Daiki Koizumi, MichioSonoda, 酒井 拓史]
通讯作者: 酒井 拓史
DOI: 10.1017/s1474748013000315
发表时间: 2013-01
期刊: Journal of the Institute of Mathematics of Jussieu
影响因子: 0.9
作者: [Hiroshi Sakai;B. Velickovic]
通讯作者: Hiroshi Sakai;B. Velickovic
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