Erdős problem 598

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?

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

598.lean

Retained formal statement1 of 1

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?

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

OpenStatement only, no proof