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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2604.23433 |
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| _version_ | 1866915958731309056 |
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| author | Duman, Necdet Gönül, Özge Kaya, Burak Saxena, Jayatra Tamer, Yiğithan |
| author_facet | Duman, Necdet Gönül, Özge Kaya, Burak Saxena, Jayatra Tamer, Yiğithan |
| contents | This paper is a contribution to the investigation of closed partition relations for pairs of countable ordinals. As our main result, we prove that \[ω^4 \cdot (n-2)+1 < R^{cl}(ω\cdot n+1,3)<ω^5\] for every integer $n \geq 3$. This result significantly improves the existing upper and lower bounds for these closed Ramsey numbers. In addition, we prove that \[ω^θ\nrightarrow_{cl} (ω^α,3)^2\] whenever $1 \leq α\leq θ<ω_1$ satisfy $θ< R(α,3)$. This result asymptotically improves the existing lower bounds for $R^{cl}(ω^n,3)$ and slightly strengthens the existing necessary condition for being a topological partition ordinal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23433 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On closed Ramsey numbers of small countable ordinals Duman, Necdet Gönül, Özge Kaya, Burak Saxena, Jayatra Tamer, Yiğithan Logic Combinatorics 03E02 (Primary), 03E10 (Secondary) This paper is a contribution to the investigation of closed partition relations for pairs of countable ordinals. As our main result, we prove that \[ω^4 \cdot (n-2)+1 < R^{cl}(ω\cdot n+1,3)<ω^5\] for every integer $n \geq 3$. This result significantly improves the existing upper and lower bounds for these closed Ramsey numbers. In addition, we prove that \[ω^θ\nrightarrow_{cl} (ω^α,3)^2\] whenever $1 \leq α\leq θ<ω_1$ satisfy $θ< R(α,3)$. This result asymptotically improves the existing lower bounds for $R^{cl}(ω^n,3)$ and slightly strengthens the existing necessary condition for being a topological partition ordinal. |
| title | On closed Ramsey numbers of small countable ordinals |
| topic | Logic Combinatorics 03E02 (Primary), 03E10 (Secondary) |
| url | https://arxiv.org/abs/2604.23433 |