{"title":"On the Erdős–Dushnik–Miller theorem without AC","authors":"Amitayu Banerjee, Alexa Gopaulsingh","doi":"10.4064/ba221221-6-6","DOIUrl":null,"url":null,"abstract":"In $\\mathsf {ZFA}$ (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition $\\mathsf {EDM}$ (“If $G=(V_{G}, E_{G})$ is a graph such that $V_{G}$ is uncountable,","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Polish Academy of Sciences. Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/ba221221-6-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In $\mathsf {ZFA}$ (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition $\mathsf {EDM}$ (“If $G=(V_{G}, E_{G})$ is a graph such that $V_{G}$ is uncountable,