PARTITION THEOREMS FOR SPACES OF VARIABLE WORDS

Furstenberg and Katznelson applied methods of topological dynamics to Ramsey theory, obtaining a density version of the Hales-Jewett partiti on theorem. Inspired by their methods, but using spaces of ultrafilter s instead of their metric spaces, we prove a generalization of a theor em of Carlson about variable words. We extend this result to partition s of finite or infinite sequences of variable words, and we apply thes e extensions to strengthen a partition theorem of Furstenberg and Katz nelson about combinatorial subspaces of the set of words.