Prömel–Voigt: canonical partition theorems for parameter sets

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Held copy and library card.

H. J. Prömel and B. Voigt, "Canonical partition theorems for parameter sets," Journal of Combinatorial Theory, Series A 35 (1983), no. 3, 309--327.

This paper proves a canonical (unrestricted) version of the Graham–Rothschild partition theorem for $k$-parameter sets, rather than a merely monochromatic one. After passing to a structured subspace, a coloring with arbitrarily many colors has one of a controlled set of canonical forms; the Erdős–Rado canonization theorem follows as a corollary (abstract, p. 309).