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Let be a family of sets with for all , such that for any we have finite and . Is there a -colouring of such that no is monochromatic?
Source: erdosproblems.com/602
No claim settles this problem.
Open. The site's proof-claims tab carries one partial proof claim, filed 2026-10-01, a finite criterion for Property B that its author says does not resolve the problem; the site shows no verdict and labels the problem OPEN. The filing is recorded below and gets no claim page, since it settles no instance of the question.