A new ultrafilter proof of Van der Waerden's theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914368542736384 |
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| author | Di Nasso, Mauro |
| author_facet | Di Nasso, Mauro |
| contents | 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 $β\N$, but contrarily to the other existing proofs, neither minimal nor idempotent ultrafilters are involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04043 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new ultrafilter proof of Van der Waerden's theorem Di Nasso, Mauro Logic Combinatorics Primary 05D10, Secondary 54D80 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 $β\N$, but contrarily to the other existing proofs, neither minimal nor idempotent ultrafilters are involved. |
| title | A new ultrafilter proof of Van der Waerden's theorem |
| topic | Logic Combinatorics Primary 05D10, Secondary 54D80 |
| url | https://arxiv.org/abs/2603.04043 |