Carlson and Simpson proved a theorem, which is, in a certain sense, a dual form of Ramsey's theorem. Moreover, their result can be viewed as an infinite generalization of the Graham-Rothschild partition theorem for n-parameter sets. A canonizing version of the Graham-Rothschild theorem has been given by Voigt and the author, extending the original partition theorem for n-parameter sets much in the same way as the Erdös-Rado canonization theorem extends Ramsey's theorem.

The purpose of our work is to establish a canonizing version of the Carlson-Simpson result. This can be regarded as a dual form of the Erdös-Rado canonization theorem. As corollaries, we obtain results which are of interest in their own sake.

The paper has been finally published as a joint paper with S. G. Simpson and B. Voigt under the same title in J. Combin. Theory Ser. A 42 (1986), 159-178.