Partition theorems for Ketonen-Solovay largeness
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915786490118144 |
|---|---|
| author | Houérou, Quentin Le Patey, Ludovic |
| author_facet | Houérou, Quentin Le Patey, Ludovic |
| contents | We develop the framework of $α$-largeness introduced by Ketonen and Solovay, by proving a partition theorem for $α$-large sets with $α< ε_0$ which generalizes theorems from Ketonen and Solovay and from Bigorajska and Kotlarski. We also prove that for every $ω^{nk+3}$-large set $X$ with $\min X \geq 18$, every coloring $f : [X]^2 \to k$ admits an $ω^n$-large $f$-homogeneous subset. This bound is tight, up to an additive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partition theorems for Ketonen-Solovay largeness Houérou, Quentin Le Patey, Ludovic Logic Combinatorics 03F15, 05D10 (Primary) 05C55 (Secondary) We develop the framework of $α$-largeness introduced by Ketonen and Solovay, by proving a partition theorem for $α$-large sets with $α< ε_0$ which generalizes theorems from Ketonen and Solovay and from Bigorajska and Kotlarski. We also prove that for every $ω^{nk+3}$-large set $X$ with $\min X \geq 18$, every coloring $f : [X]^2 \to k$ admits an $ω^n$-large $f$-homogeneous subset. This bound is tight, up to an additive constant. |
| title | Partition theorems for Ketonen-Solovay largeness |
| topic | Logic Combinatorics 03F15, 05D10 (Primary) 05C55 (Secondary) |
| url | https://arxiv.org/abs/2602.08778 |