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Claim. Chang's Theorem (p. 396) is the relation $\omega^\omega\to(\omega^\omega,3)^2$: whenever the pairs from the ordinal $\omega^\omega$ are split into two classes, either some three elements have all their pairs in the first class or some subset of order type $\omega^\omega$ has all its pairs in the second. In the reading $\alpha=\omega^\beta$ of Problem 592 (its Formulation) this is the case $\beta=\omega$, which therefore has the property. The proof (pp. 403--405) is an induction on four lemmas, the Normal Form, Super Form, Transitivity and Well-Foundedness Lemmas, proved in §§ 2--5, with Erdős's $\omega^{2n+1}\to(\omega^{n+1},4)^2$ as an outside input. On p. 397 the paper poses the general question in the form $\omega^{\omega^\alpha}\to(\omega^{\omega^\alpha},3)^2$ for $\alpha<\omega_1$ (problems_p397), of which its theorem is the case $\alpha=1$. The paper is C. C. Chang, A Partition Theorem for the Complete Graph on $\omega^\omega$, J. Combinatorial Theory (A) 12 (1972), 396--452, DOI 10.1016/0097-3165(72)90105-7, the site's [Ch72], received 24 February 1970; the publisher's record dates the issue to May 1972, and the page name carries the first day of that month, since the record gives no day. It is paged on the library's source card.

Covers. The exponent $\beta=\omega$: the property holds. Not covered: every other $\beta$, and the extension to larger cliques $\omega^\omega\to(\omega^\omega,m)^2$, which the paper's footnote 1 reports from Milner by letter.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in the Journal of Combinatorial Theory, Series A, volume 12. The site labels the problem OPEN, and its commentary crediting Chang on an open problem is not an acceptance, so no reviewed evidence is listed.

Read depth. The theorem, the four lemma statements and the proof of the theorem from them are checked; the proofs of the lemmas were read for structure only.