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Erdős problem 70

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Erdős Problem 70: Let c\mathfrak{c} be the cardinality of the continuum, let β\beta be a countable ordinal, and let 2≤n<ω2 \le n < \omega. Is it true that c→(β,n)23\mathfrak{c} \to (\beta, n)^3_2?

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6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

70.lean

Retained formal statement6 of 6

Monotonicity of `OrdinalCardinalRamsey3`: If OrdinalCardinalRamsey3 α β c holds and β′≤β\beta' \le \beta, c′≤cc' \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
∀ {α β β' : Ordinal.{u}} {c c' : Cardinal.{u}},  Erdos70.OrdinalCardinalRamsey3 α β c → β' ≤ β → c' ≤ c → Erdos70.OrdinalCardinalRamsey3 α β' c'
TestStatement only, no proof