On the deductive strength of the Erdős-Dushnik-Miller theorem and two order-theoretic principles

DOI10.1007/s00605-023-01933-zOpenAlexW4391174070MaRDI QIDQ6120274

Eleftherios Tachtsis

Publication date: 20 February 2024

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-023-01933-z

zbMATH Keywords

graphantichainpartially ordered setchainAxiom of Choicepermutation modelKurepa's theoremErdős-Dushnik-Miller theoremweak Axioms of Choice

Mathematics Subject Classification ID

Partial orders, general (06A06) Combinatorics of partially ordered sets (06A07) Consistency and independence results (03E35) Axiom of choice and related propositions (03E25) Infinite graphs (05C63)

Cites Work

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• Several results on compact metrizable spaces in \(\mathbf{ZF} \)
• On a theorem of Kurepa for partially ordered sets and weak choice
• ON RAMSEY’S THEOREM AND THE EXISTENCE OF INFINITE CHAINS OR INFINITE ANTI-CHAINS IN INFINITE POSETS
• An independence result concerning the axiom of choice
• The Law of Infinite Cardinal Addition is Weaker than the Axiom of Choice
• The axiom of choice and linearly ordered sets
• Ramsey's theorem in the hierarchy of choice principles
• The axiom of choice for linearly ordered families
• Some applications of the notions of forcing and generic sets
• The independence of the axiom of choice from the Boolean prime ideal theorem
• The axiom of choice
• On the Erdős–Dushnik–Miller theorem without AC
• Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC

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