Erdős problem 70 · problems.science

Erdős Problem 70: Let $\mathfrak{c}$ be the cardinality of the continuum, let $\beta$ be a countable ordinal, and let $2 \le n < \omega$ . Is it true that $\mathfrak{c} \to (\beta, n)^3_2$ ?

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70.lean

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Erdős Problem 70: Let $\mathfrak{c}$ be the cardinality of the continuum, let $\beta$ be a countable ordinal, and let $2 \le n < \omega$ . Is it true that $\mathfrak{c} \to (\beta, n)^3_2$ ?

Note: The cases $n \le 3$ are trivially true (see omega_three), so the genuine content of the conjecture begins at $n = 4$ .

FormalConjectures/ErdosProblems/70.leanErdos70.erdos_703 linesExact file

1True ↔2  ∀ (β : Ordinal.{0}) (n : ℕ),3    β.card ≤ Cardinal.aleph0 → 2 ≤ n → Erdos70.OrdinalCardinalRamsey3 Cardinal.continuum.ord β ↑n

OpenStatement only, no proof

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