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Claim. Theorem 3 of Saharon Shelah and Lee Stanley, A theorem and some consistency results in partition calculus, Ann. Pure Appl. Logic 36 (1987), no. 2, 119--152, stated on p. 119 and proved in §3 (pp. 139--144), reads: if ZFC is consistent, then so is ZFC + $\aleph_{\mathfrak c^+}\not\to(\aleph_{\mathfrak c^+},\aleph_1)^2$. The cardinal $\lambda=\aleph_{\mathfrak c^+}$ meets both hypotheses of the Statement of Problem 1220 in ZFC. It is singular, of cofinality $\mathfrak c^+$, and its cofinality is $\aleph_0$-inaccessible, since $\mu^{\aleph_0}\le\mathfrak c^{\aleph_0}=\mathfrak c$ for $\mu<\mathfrak c^+$. The cardinal itself is $\aleph_0$-inaccessible by Shelah's ZFC theorem that $\mu^{\aleph_0}<\aleph_{\mathfrak c^+}$ for every $\mu<\aleph_{\mathfrak c^+}$, which the paper's historical remarks (p. 125) record from S. Shelah, A note on cardinal exponentiation, J. Symbolic Logic 45 (1980), 56--66. So in the model of Theorem 3 a singular cardinal $\lambda$ with $\lambda$ and $\mathrm{cf}(\lambda)$ both $\aleph_0$-inaccessible fails $\lambda\to(\lambda,\aleph_1)^2$, the universal statement is false there, and ZFC, if consistent, does not prove it. The paper treats the instance at $\aleph_{\mathfrak c^+}$, which its p. 125 traces to Problem 35.5 of the book of Erdős, Hajnal, Máté and Rado, and states no conclusion about the universal question; the step to it is the bound above.

Covers. The not-provable side of Problem 1220, relative to the consistency of ZFC: ZFC does not prove that every singular $\lambda$ with $\lambda$ and $\mathrm{cf}(\lambda)$ both $\aleph_0$-inaccessible satisfies $\lambda\to(\lambda,\aleph_1)^2$. It settles that side only; it does not show that ZFC fails to refute the statement, and one side alone leaves the question open. The not-disprovable side is on Erdős, Hajnal and Rado's page, and the two pages together settle the problem as independent of ZFC. Bae's pending claim asserts the same not-provable side.

Acceptance. Refereed: the result is a journal paper in the Annals of Pure and Applied Logic, volume 36 (1987), received 3 March 1986 and communicated by A. Nerode. The DOI record gives only the year, so this page's date is the first day of 1987. The site labels the problem OPEN, so no curator acceptance is listed. This page states Theorem 3 and the remarks of p. 125 as the Shelah archive's copy of the published version (Sh:258) prints them; the proof in §3 is not reviewed in this corpus.

Depends on. No other wiki page; the claim rests on the paper above and the 1980 bound it records.