Infinite combinatorial principles and compact cardinals

无限组合原理和紧基数

• 批准号: 20540142
• 负责人: ABE Yoshihiro
• 金额: $ 1.75万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540142/
• 关键词: Pκλ; ineffability; 分割の性質; stationary set; コンパクト基数; cofinality; イデアル; reflection; stationary; P(λ); unbranched proerty; compact space; orthocompact; normal space; Lindelof space; P_κλ; projection; regular space; 強制法; indescribability

We proved several facts in the combinatorial set theory on Pκλ={x⊂λ:|x|<κ}, the set of all subsets of λ with cardinality less than κ. For instance :(1) If the cofinality ofλis smaller thanκ, then there exists a stationary subset S of Pκλsuch that every stationary subset of S can be splitted intoλ^+many disjoint stationary sets.(2) If the cofinality ofλis not smaller thanκand there is a weakly normal ideal onPκλ, then the cardinality of PκλisMax(2^<κ,λ).(3) Suppose that the cofinality ofλis not smaller thanκand X is a subset ofPκλ. Then, X is ineffable if and only if it has the partition property.

我们在pκλ= {x⊂λ：| x | <κ}的组合集理论中提供了几个事实，这是λ的所有子集的集合，基数小于κ。例如：（1）如果λis的辅助性小于κ，则存在一个固定的子集，pκλssuce是，s的每个固定子集都可以分为λ^+λ^+许多不相交的静止集。假设λis的辅助性不小于κ和x是Pκλ的子集。然后，仅当它具有分区属性时，x是无法算法的。

项目成果

Orderability of subspaces of well-orderable topological spaces

可有序拓扑空间的子空间的可有序性

• 发表时间: 2010
• 期刊: Top.Appl. 157
• 作者: Y. Hirata;N. Kemoto
• 通讯作者: N. Kemoto

Ineffability of P_κλ for λ with small cofinality

对于具有小共尾性的 λ，P_κλ 的不可表达性

• 发表时间: 2008
• 期刊: Journal of Mathematical Society of Japan 60巻
• 作者: Mariko Yasugi;Masako Washihara;森真;Toshimichi Usuba
• 通讯作者: Toshimichi Usuba

Fodor-type Reflection Principle and reflection of metrizability and meta-Lindelofness

Fodor型反射原理以及可测量性和元Lindelofness的反射

• 发表时间: 2009
• 期刊: Special Issue of "Topology and its Applications" dedicated to the Proceedings of the Conference "Advances in Set-Theoretic Topology" (in Honour of Tsugunori Nogura on his 60th Birthday)
• 作者: Sakae Fuchino;Istvan Juhasz;Lajos Soukup;Zoltan Szentmiklossy and Toshimichi Usuba
• 通讯作者: Zoltan Szentmiklossy and Toshimichi Usuba

順序数の積の位相的性質

序数乘积的拓扑性质

• 发表时间: 2010
• 作者: Takakazu Mori;Mariko Yasugi;Yoshiki Tsujii;平田康史
• 通讯作者: 平田康史

Orthocompactness versus normality in hyperspaces

超空间中的正交紧性与正态性

• 发表时间: 2012
• 期刊: Top. Appl.
• 作者: Yasushi Hirata;Nobuyuki Kemoto;Yukinobu Yajima;Kazuhiro Kuwae;皆本晃弥;Y. Hirata and N. Kemoto
• 通讯作者: Y. Hirata and N. Kemoto