#####
Séminaire Lotharingien de Combinatoire, B10d (1984).

[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 244/S-110, p.
102-104.]

# Hans Jürgen Prömel

# A Dual Form of Erdös-Rado's Canonization Theorem

**Abstract.**
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.