On Borel subsets of generalized Baire spaces
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_ | 1866911245336051712 |
|---|---|
| author | Hyttinen, Tapani Moreno, Miguel Väänänen, Jouko |
| author_facet | Hyttinen, Tapani Moreno, Miguel Väänänen, Jouko |
| contents | We develop Descriptive Set Theory in Generalized Baire Spaces without assuming $κ^{<κ}=κ$. We point out that without this assumption the basic topological concepts of these spaces have to be slightly modified in order to obtain a meaningful theory. This modification has no effect if $κ^{<κ}=κ$. After developing the basic theory we apply it to the question whether the orbits of models of a fixed cardinality $κ$ in the space $κ^κ$ are $κ$-Borel in our generalized sense. It turns out that this question depends, as is the case when $κ^{<κ}=κ$, on stability theoretic properties (structure vs. non-structure) of the first order theory of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Borel subsets of generalized Baire spaces Hyttinen, Tapani Moreno, Miguel Väänänen, Jouko Logic 03E15, 03C45 We develop Descriptive Set Theory in Generalized Baire Spaces without assuming $κ^{<κ}=κ$. We point out that without this assumption the basic topological concepts of these spaces have to be slightly modified in order to obtain a meaningful theory. This modification has no effect if $κ^{<κ}=κ$. After developing the basic theory we apply it to the question whether the orbits of models of a fixed cardinality $κ$ in the space $κ^κ$ are $κ$-Borel in our generalized sense. It turns out that this question depends, as is the case when $κ^{<κ}=κ$, on stability theoretic properties (structure vs. non-structure) of the first order theory of the model. |
| title | On Borel subsets of generalized Baire spaces |
| topic | Logic 03E15, 03C45 |
| url | https://arxiv.org/abs/2507.15427 |