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 statement6 of 6

Monotonicity of `OrdinalCardinalRamsey3`: If OrdinalCardinalRamsey3 α β c holds and $\beta' \le \beta$ , $c' \le c$ , then OrdinalCardinalRamsey3 α β' c' also holds.

This allows us to deduce weaker partition results from stronger ones.

FormalConjectures/ErdosProblems/70.leanErdos70.erdos_70.variants.ordinalCardinalRamsey3_mono2 linesExact file

1∀ {α β β' : Ordinal.{u}} {c c' : Cardinal.{u}},2  Erdos70.OrdinalCardinalRamsey3 α β c → β' ≤ β → c' ≤ c → Erdos70.OrdinalCardinalRamsey3 α β' c'

TestStatement only, no proof

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