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 statement5 of 6

First open case beyond Erdős–Rado: $\mathfrak{c} \to (\omega \cdot 2, 4)^3_2$ .

Erdős and Rado proved $\mathfrak{c} \to (\omega + n, 4)^3_2$ for every finite $n \ge 2$ (see erdos_rado), which covers all red ordinals below $\omega \cdot 2 = \omega + \omega$ . This variant asks whether the result extends to $\beta = \omega \cdot 2$ , the simplest countable ordinal not covered by their theorem.

FormalConjectures/ErdosProblems/70.leanErdos70.erdos_70.variants.omega_times_two_four1 lineExact file

1True ↔ Erdos70.OrdinalCardinalRamsey3 Cardinal.continuum.ord (Ordinal.omega0 * 2) 4

OpenStatement only, no proof

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