ON RAMSEY’S THEOREM AND THE EXISTENCE OF INFINITE CHAINS OR INFINITE ANTI-CHAINS IN INFINITE POSETS

DOI10.1017/jsl.2015.47zbMath1342.03036OpenAlexW2467421883MaRDI QIDQ2805042

Eleftherios Tachtsis

Publication date: 9 May 2016

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/jsl.2015.47

zbMATH Keywords

partially ordered setsaxiom of choiceRamsey's theoremPincus' transfer theoremsweak forms of the axiom of choiceanti-chains in partially ordered setschains in partially ordered setsFraenkel-Mostowski (FM) permutation models for ZFA

Mathematics Subject Classification ID

Consistency and independence results (03E35) Ramsey theory (05D10) Axiom of choice and related propositions (03E25)

Related Items (12)

On the minimal cover property and certain notions of finite ⋮ On the comparability of cardinals in the absence of the axiom of choice ⋮ Hindman's theorem and choice ⋮ On the deductive strength of the Erdős-Dushnik-Miller theorem and two order-theoretic principles ⋮ Łoś's theorem and the axiom of choice ⋮ Hindman’s theorem in the hierarchy of choice principles ⋮ Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC ⋮ On variants of the principle of consistent choices, the minimal cover property and the 2-compactness of generalized Cantor cubes ⋮ Properties of the atoms in finitely supported structures ⋮ On Ramsey choice and partial choice for infinite families of \(n\)-element sets ⋮ On a theorem of Kurepa for partially ordered sets and weak choice ⋮ On the interrelation of a theorem of Juhász and certain weak axioms of choice

Cites Work

• Ramsey's theorem and König's lemma
• Set theory. An introduction to large cardinals
• On Ramsey's theorem and the axiom of choice
• Partial choice functions for families of finite sets
• The axiom of choice
• Unnamed Item

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