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Additive and multiplicative Ramsey theorems in \(\mathbb{N}\)—some elementary results. (English) Zbl 0794.05127

The paper gives a new proof for the eminent theorem of Hindman that taking a finite partition of the set of positive integers one can find a partition class which contains an infinite sequence and all of its finite sums and another infinite sequence of its finite products. There are partitions where those two sequences are different. The proof is elementary (but not easy at all) and avoids the use of the Axiom of Choice.

MSC:

05D10 Ramsey theory
11B25 Arithmetic progressions
20M99 Semigroups
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References:

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