Three forms of the Erdős-Dushnik-Miller Theorem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916687045984256 |
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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 |