Trivial Isomorphisms between Reduced Products
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916457155133440 |
|---|---|
| author | De Bondt, Ben Farah, Ilijas Vignati, Alessandro |
| author_facet | De Bondt, Ben Farah, Ilijas Vignati, Alessandro |
| contents | We introduce a general method for showing under weak forcing axioms that reduced products of countable models of a theory $T$ have as few automorphisms as possible. We show that such forcing axioms imply that reduced products of countably infinite or finite fields, linear orders, trees, or random graphs have only trivial automorphisms. We also show that Todorčević's Open Colouring Axiom, $\mathsf{OCA}_{\mathrm{T}}$, implies that all automorphisms of $\mathcal{P}(\mathbb{N})/{\mathrm{Fin}}$ are trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06731 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trivial Isomorphisms between Reduced Products De Bondt, Ben Farah, Ilijas Vignati, Alessandro Logic 03E50, 03E35, 03E75 We introduce a general method for showing under weak forcing axioms that reduced products of countable models of a theory $T$ have as few automorphisms as possible. We show that such forcing axioms imply that reduced products of countably infinite or finite fields, linear orders, trees, or random graphs have only trivial automorphisms. We also show that Todorčević's Open Colouring Axiom, $\mathsf{OCA}_{\mathrm{T}}$, implies that all automorphisms of $\mathcal{P}(\mathbb{N})/{\mathrm{Fin}}$ are trivial. |
| title | Trivial Isomorphisms between Reduced Products |
| topic | Logic 03E50, 03E35, 03E75 |
| url | https://arxiv.org/abs/2307.06731 |