A new ultrafilter proof of Van der Waerden’s Theorem
Keywords:
Partition regularity, Van der Waerden’s Theorem, Algebra in the space of ultrafiltersAbstract
We present a new short proof of Van der Waerden's Theorem about the existence of arbitrarily long monochromatic arithmetic progressions. The proof uses algebra in the compact space of ultrafilters $\beta \mathbb{N}$, but contrarily to the other existing proofs, neither minimal nor idempotent ultrafilters are involved.
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