Erdős problem 598 · problems.science

Erdős Problem 598: Let $m$ be an infinite cardinal and $\kappa$ be the successor cardinal of $2^{\aleph_0}$ . Can one colour the countable subsets of $m$ using $\kappa$ many colours so that every $X \subseteq m$ with $|X| = \kappa$ contains subsets of all possible colours?

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FormalConjectures/ErdosProblems/598.lean

Formal Conjectures

FormalConjectures/ErdosProblems/598.leanErdos598.erdos_5981 lineExact file

1∀ (m : Type u_1) [Infinite m], True ↔ ∃ c, ∀ (X : Set m), Cardinal.mk ↑X = Erdos598.κ → c '' {s | ↑s ⊆ X} = Set.univ

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Erdős AI contributions wiki · 22 Apr, 2026
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Aristotle, GPT-5.4 Pro
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Przemek Chojecki
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