Separating Many Localisation Cardinals on the Generalised Baire Space
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916655509012480 |
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| author | van der Vlugt, Tristan |
| author_facet | van der Vlugt, Tristan |
| contents | Given a cofinal cardinal function $h\in{}^κκ$ for $κ$ inaccessible, we consider the dominating $h$-localisation number, that is, the least cardinality of a dominating set of $h$-slaloms such that every $κ$-real is localised by a slalom in the dominating set. It was proved in arXiv:1611.08140 that the dominating localisation numbers can be consistently different for two functions $h$ (the identity function and the power function). We will construct a $κ$-sized family of functions $h$ and their corresponding localisation numbers, and use a ${\leq}κ$-supported product of a cofinality-preserving forcing to prove that any simultaneous assignment of these localisation numbers to cardinals above $κ$ is consistent. This answers an open question from arXiv:1611.08140 . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_03256 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Separating Many Localisation Cardinals on the Generalised Baire Space van der Vlugt, Tristan Logic Given a cofinal cardinal function $h\in{}^κκ$ for $κ$ inaccessible, we consider the dominating $h$-localisation number, that is, the least cardinality of a dominating set of $h$-slaloms such that every $κ$-real is localised by a slalom in the dominating set. It was proved in arXiv:1611.08140 that the dominating localisation numbers can be consistently different for two functions $h$ (the identity function and the power function). We will construct a $κ$-sized family of functions $h$ and their corresponding localisation numbers, and use a ${\leq}κ$-supported product of a cofinality-preserving forcing to prove that any simultaneous assignment of these localisation numbers to cardinals above $κ$ is consistent. This answers an open question from arXiv:1611.08140 . |
| title | Separating Many Localisation Cardinals on the Generalised Baire Space |
| topic | Logic |
| url | https://arxiv.org/abs/2203.03256 |