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Statement

Problem 8 (printed pp. 225--226), quoted: "Is it true that for every infinite $m$ one can color the countable subsets of $m$ by $(2^{\aleph_0})^+$ colors so that every subset of size $(2^{\aleph_0})^+$ gets subsets of all the colors?"

The paper gives no proof or partial result.

Source. P. Erdős, Some problems on finite and infinite graphs, Logic and Combinatorics (Arcata, Calif., 1985), Contemp. Math. 65, Amer. Math. Soc. (1987), 223--228; Problem 8, pp. 225--226, PDF pp. 3--4 of the Rényi archive's scan (printed p. $n$ = PDF p. $n-222$), read on the rendered page images. The edition read is identified in the source digest.

Read depth. Claims checked: the question was read clause by clause on the page images. A question has no proof to check.

Proof pointer

None in the source.

Dependencies

None.

Bears on

• Problem 598: the question is this problem's; the print quantifies over every infinite $m$, where the site fixes $m$. The paper records no result on it.