Three forms of the Erdős-Dushnik-Miller Theorem

Fuente: arXiv
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Autori principali: Howard, Paul, Tachtsis, Eleftherios
Natura: Preprint
Pubblicazione: 2024
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author Howard, Paul
Tachtsis, Eleftherios
author_facet Howard, Paul
Tachtsis, Eleftherios
contents We continue the study of the Erdős-Dushnik-Miller theorem (A graph with an uncountable set of vertices has either an infinite independent set or an uncountable clique) in set theory without the axiom of choice. We show that there are three inequivalent versions of this theorem and we give some results about the positions of these versions in the deductive hierarchy of weak choice principles.
format Preprint
id arxiv_https___arxiv_org_abs_2410_18229
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Three forms of the Erdős-Dushnik-Miller Theorem
Howard, Paul
Tachtsis, Eleftherios
Logic
03E25 (Primary) 03E35, 05C63 (Secondary)
We continue the study of the Erdős-Dushnik-Miller theorem (A graph with an uncountable set of vertices has either an infinite independent set or an uncountable clique) in set theory without the axiom of choice. We show that there are three inequivalent versions of this theorem and we give some results about the positions of these versions in the deductive hierarchy of weak choice principles.
title Three forms of the Erdős-Dushnik-Miller Theorem
topic Logic
03E25 (Primary) 03E35, 05C63 (Secondary)
url https://arxiv.org/abs/2410.18229