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For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial can be chosen from a given subsemigroup and one can prescribe the occurring powers. A multidimensional version is… (More)

- Rudi Hirschfeld
- 2008

A set of natural numbers will be called harmonic if the reciprocals of its elements form a divergent series. An ultrafilter of the natural numbers will he called harmonic if all each members are harmonic sets. The harmonic ultrafilters are shown to constitute a compact semigroup under the Glazer addition and its smallest ideal is obtained. This paper is an… (More)

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