Lionel Nguyen Van Thé, Université d'Aix-Marseille
Revisiting the canonical Ramsey theorem for finite vector spaces
The infinite Ramsey theorem (1931) asserts that for every integer m, if the collection of all m-subsets of natural numbers is finitely colored, then there exists an infinite subset whose m-subsets are all of the same color. This result does not hold anymore if the number of colors is not finite, but Erdös and Rado (1950) showed that there is still an infinite subset where the coloring takes a very particular form, called "canonical". Both of these results admit appropriate finite forms which hold in the context of vector spaces instead of sets by results of Graham-Leeb-Rothschild (1972) and Voigt (1984). The purpose of this talk will be to present a new approach to this latter result.
MC 5403