{"title":"关于没有AC的Erdős-Dushnik-Miller定理","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":"{\"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}","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}
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,
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