Partitions of Baire space into compact sets
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909603155935232 |
|---|---|
| author | Fischer, Vera Schembecker, Lukas |
| author_facet | Fischer, Vera Schembecker, Lukas |
| contents | Under $\text{CH}$ we construct a partition of Baire space into compact sets, which is indestructible by countably supported iteration and product of Sacks forcing of any length, answering a question of Newelski. Further, we present an in-depth isomorphism-of-names argument for $\text{spec}(\mathfrak{a}_\text{T}) = \{\aleph_1, \mathfrak{c}\}$ in the product-Sacks model. Finally, we prove that Shelah's ultrapower model for the consistency of $\mathfrak{d} < \mathfrak{a}$ also satisfies $\mathfrak{a} = \mathfrak{a}_\text{T}$. Thus, consistently $\aleph_1 < \mathfrak{d} < \mathfrak{a} = \mathfrak{a}_\text{T}$ holds relative to a measurable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09994 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partitions of Baire space into compact sets Fischer, Vera Schembecker, Lukas Logic Under $\text{CH}$ we construct a partition of Baire space into compact sets, which is indestructible by countably supported iteration and product of Sacks forcing of any length, answering a question of Newelski. Further, we present an in-depth isomorphism-of-names argument for $\text{spec}(\mathfrak{a}_\text{T}) = \{\aleph_1, \mathfrak{c}\}$ in the product-Sacks model. Finally, we prove that Shelah's ultrapower model for the consistency of $\mathfrak{d} < \mathfrak{a}$ also satisfies $\mathfrak{a} = \mathfrak{a}_\text{T}$. Thus, consistently $\aleph_1 < \mathfrak{d} < \mathfrak{a} = \mathfrak{a}_\text{T}$ holds relative to a measurable. |
| title | Partitions of Baire space into compact sets |
| topic | Logic |
| url | https://arxiv.org/abs/2312.09994 |