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Logic and foundations
Erdős problem 70 - omega times two four
**First open case beyond Erdős–Rado**: c→(ω⋅2,4)23.
Erdős and Rado proved c→(ω+n,4)23
for every finite
n≥2
(see
erdos_rado
), which covers all red ordinals below
ω⋅2=ω+ω
.
This variant asks whether the result extends to
β=ω⋅2
, the simplest
countable ordinal not covered by their theorem.
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Erdős problem 70 - omega times two four · Conjectures.io