A Dual Form of Erdös-Rado's Canonization Theorem
Séminaire lotharingien de combinatoire, Tome 10 (1984)
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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.
@article{SLC_1984_10_a3,
author = {Hans J\"urgen Pr\"omel},
title = {A {Dual} {Form} of {Erd\"os-Rado's} {Canonization} {Theorem}},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {10},
year = {1984},
url = {http://geodesic.mathdoc.fr/item/SLC_1984_10_a3/}
}
Hans Jürgen Prömel. A Dual Form of Erdös-Rado's Canonization Theorem. Séminaire lotharingien de combinatoire, Tome 10 (1984). http://geodesic.mathdoc.fr/item/SLC_1984_10_a3/