We show that by only assuming Schur’s Theorem and the existence of a non- principal ultrafilter, one can directly prove that in every finite coloring of N there exist infinite disjoint sets A,B such that all elements of A∪B∪(A+B) are monochromatic. This gives a partial answer to a question posed by N. Hindman, I. Leader, and D. Strauss in 2003. In the last section we propose a formalization of that open question in purely topological terms.
From Schur’s Theorem to the Pairwise Sum Theorem
Mauro Di NassoCo-primo
;Renling JinCo-primo
2025-01-01
Abstract
We show that by only assuming Schur’s Theorem and the existence of a non- principal ultrafilter, one can directly prove that in every finite coloring of N there exist infinite disjoint sets A,B such that all elements of A∪B∪(A+B) are monochromatic. This gives a partial answer to a question posed by N. Hindman, I. Leader, and D. Strauss in 2003. In the last section we propose a formalization of that open question in purely topological terms.File in questo prodotto:
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