The celebrated Theorem of van der Waerden is very simple to state as well as non trivial to prove: If is finitely coloured, there exists a monochrome set which contains arbitrarily long arithmetic progressions. The corresponding statement about geometric progressions is also known to be true. We use the algebraic structure of the Stone-Cech-Compactification of to derive common extensions of these results: For example we show that for there exist such that for all .

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