不可数集、幂集和全域之间的结构相似性

Pub Date : 2022-03-06 DOI:10.1002/malq.202100010

Athanassios Tzouvaras

{"title":"不可数集、幂集和全域之间的结构相似性","authors":"Athanassios Tzouvaras","doi":"10.1002/malq.202100010","DOIUrl":null,"url":null,"abstract":"We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras <math>\n <semantics>\n <mrow>\n <mi>P</mi>\n <mo>(</mo>\n <mi>κ</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {P}(\\kappa )$</annotation>\n </semantics></math>, for a regular cardinal κ, and <math>\n <semantics>\n <mrow>\n <mi>C</mi>\n <mo>(</mo>\n <mi>V</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {C}(V)$</annotation>\n </semantics></math> (the class of subclasses of the universe V), endowed with some ideals, especially the ideal <math>\n <semantics>\n <msup>\n <mrow>\n <mo>[</mo>\n <mi>κ</mi>\n <mo>]</mo>\n </mrow>\n <mrow>\n <mo><</mo>\n <mi>κ</mi>\n </mrow>\n </msup>\n <annotation>$[\\kappa ]^{<\\kappa }$</annotation>\n </semantics></math> for <math>\n <semantics>\n <mrow>\n <mi>P</mi>\n <mo>(</mo>\n <mi>κ</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {P}(\\kappa )$</annotation>\n </semantics></math>, and the ideal of sets V for <math>\n <semantics>\n <mrow>\n <mi>C</mi>\n <mo>(</mo>\n <mi>V</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {C}(V)$</annotation>\n </semantics></math>.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some structural similarities between uncountable sets, powersets and the universe\",\"authors\":\"Athanassios Tzouvaras\",\"doi\":\"10.1002/malq.202100010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras <math>\\n <semantics>\\n <mrow>\\n <mi>P</mi>\\n <mo>(</mo>\\n <mi>κ</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathcal {P}(\\\\kappa )$</annotation>\\n </semantics></math>, for a regular cardinal κ, and <math>\\n <semantics>\\n <mrow>\\n <mi>C</mi>\\n <mo>(</mo>\\n <mi>V</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathcal {C}(V)$</annotation>\\n </semantics></math> (the class of subclasses of the universe V), endowed with some ideals, especially the ideal <math>\\n <semantics>\\n <msup>\\n <mrow>\\n <mo>[</mo>\\n <mi>κ</mi>\\n <mo>]</mo>\\n </mrow>\\n <mrow>\\n <mo><</mo>\\n <mi>κ</mi>\\n </mrow>\\n </msup>\\n <annotation>$[\\\\kappa ]^{<\\\\kappa }$</annotation>\\n </semantics></math> for <math>\\n <semantics>\\n <mrow>\\n <mi>P</mi>\\n <mo>(</mo>\\n <mi>κ</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathcal {P}(\\\\kappa )$</annotation>\\n </semantics></math>, and the ideal of sets V for <math>\\n <semantics>\\n <mrow>\\n <mi>C</mi>\\n <mo>(</mo>\\n <mi>V</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathcal {C}(V)$</annotation>\\n </semantics></math>.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/malq.202100010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202100010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们在不可数基数或幂集与所有集合的类V之间建立了一些相似/类比。它们主要涉及布尔代数P (κ)$ \mathcal {P}(\kappa)$，对于正则基数κ和C (V)$ \mathcal {C}(V)$(宇宙V的子类的类)，它们被赋予了一些理想。尤其是理想的[κ] <κ $[\kappa]^{<\kappa}$对于P (κ)$ \mathcal {P}(\kappa)$，以及集合V对于C (V)$ \mathcal {C}(V)$的理想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Some structural similarities between uncountable sets, powersets and the universe

We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras $P (κ)$ , for a regular cardinal κ, and $C (V)$ (the class of subclasses of the universe V), endowed with some ideals, especially the ideal ${[κ]}^{< κ}$ for $P (κ)$ , and the ideal of sets V for $C (V)$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助