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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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

70.lean

Retained formal statement2 of 6

Erdős–Rado partial result: $\mathfrak{c} \to (\omega + n, 4)^3_2$ for any $2 \le n < \omega$ . Positive partial answer to Problem 70 with $\beta = \omega + n$ and the blue side fixed at $4$ .

FormalConjectures/ErdosProblems/70.leanErdos70.erdos_70.variants.erdos_rado1 lineExact file

1∀ (n : ℕ), 2 ≤ n → Erdos70.OrdinalCardinalRamsey3 Cardinal.continuum.ord (Ordinal.omega0 + ↑n) 4

SolvedStatement only, no proof

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