Reflection principles on stationarity and possible extensions of the axiom system of set thoery

集合论公理系统的平稳性反思原理及其可能的扩展

• 批准号: 21540150
• 负责人: FUCHINO Sakae
• 金额: $ 2.75万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540150/
• 关键词: 数学基礎論; 反映原理; Fodor-type Reflection Principle; Rado's conjecture; chromatic number; list-chromatic number; coloring number; 位相空間; 無限グラフ; ブール代数; 距離付け可能性; coloring Number; openly generatedなブール代数; Coloring Number; Openly generatedなブール代数

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.

在这个研究项目中，我们研究了所谓的fodor型反射原理（FRP），它位于序数集合的平稳反射和可数序数集合的平稳反射之间。我们证明了FRP等同于许多“数学”反射原理，这些原理被称为Fleissner公理r的结果。我们还证明FRP暗示了Shelah的强假设，并获得了包括FRP在内的反射原理之间的含义和非含义的几乎完整的图像。

项目成果

Openly generated Boolean algebras and the Fodor-type Reflection Principle

公开生成的布尔代数和 Fodor 型反射原理

• 发表时间: 2011
• 期刊: Fundamenta Mathematicae
• 影响因子: 0.6
• 作者: Sakae Fuchino;Assaf Rinot
• 通讯作者: Assaf Rinot

R.Dedekindの数学の基礎付けと集合論の公理化

R. Dedekind 的数学基础和集合论的公理化

• 发表时间: 2011
• 期刊: 京都大学数理解析研究所講究録
• 作者: 川本啓太;石山圭亮;宮内肇;Sakae Fuchino;渕野昌
• 通讯作者: 渕野昌

Fodor-type Reflection Principle and its' mathematical', characterizations

福多尔型反射原理及其“数学”、表征

• 发表时间: 2009
• 作者: M.Asano;M.Ohya;Y.Tanaka;A.Khrennikov;I.Basieva;神保雅一;Sakae Fuchino
• 通讯作者: Sakae Fuchino

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

Fodor-type Reflection Principle and Balogh's reflection theorems

Fodor型反射原理和Balogh反射定理

• 发表时间: 2010
• 期刊: 京都大学数理解析研究所講究録
• 作者: 平田直樹;宮内肇;三澤哲也;Nobuyuki Kemoto and Yukinobu Yajima;Sakae Fuchino
• 通讯作者: Sakae Fuchino