A footnote to the KPT theorem in structural Ramsey theory
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909946344374272 |
|---|---|
| author | Cameron, Peter J. Lashkarighouchani, Siavash |
| author_facet | Cameron, Peter J. Lashkarighouchani, Siavash |
| contents | The celebrated theorem of Kechris, Pestov and Todorčević connecting structural Ramsey theory with topological dynamics has as a consequence that the Fra\"ıssé limit of a Ramsey class of non-trivial finite relational structures has a reduct which is a total order; this implies an earlier result of Nešetřil, according to which the structures in such a class are rigid (have trivial automorphism groups). In this paper, we give an alternative proof of this fact. If $\mathcal{C}$ is a Fra\"ıssé class of rigid structures over a finite relational language, then either the Fra\"ıssé limit of $\mathcal{C}$ has a reduct which is a total order, or there is an explicit failure of the Ramsey property involving a pair $(A,B)$ of structures in $\mathcal{C}$ with $|A|=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A footnote to the KPT theorem in structural Ramsey theory Cameron, Peter J. Lashkarighouchani, Siavash Logic Combinatorics 05C55 The celebrated theorem of Kechris, Pestov and Todorčević connecting structural Ramsey theory with topological dynamics has as a consequence that the Fra\"ıssé limit of a Ramsey class of non-trivial finite relational structures has a reduct which is a total order; this implies an earlier result of Nešetřil, according to which the structures in such a class are rigid (have trivial automorphism groups). In this paper, we give an alternative proof of this fact. If $\mathcal{C}$ is a Fra\"ıssé class of rigid structures over a finite relational language, then either the Fra\"ıssé limit of $\mathcal{C}$ has a reduct which is a total order, or there is an explicit failure of the Ramsey property involving a pair $(A,B)$ of structures in $\mathcal{C}$ with $|A|=2$. |
| title | A footnote to the KPT theorem in structural Ramsey theory |
| topic | Logic Combinatorics 05C55 |
| url | https://arxiv.org/abs/2512.05684 |