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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.01418 |
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| _version_ | 1866915646951915520 |
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| author | Martínez, Juan Carlos Soukup, Lajos |
| author_facet | Martínez, Juan Carlos Soukup, Lajos |
| contents | We prove that if $λ$ is a fixed uncountable cardinal and $f = \langle \ka_{\al} : \al < δ\rangle$ is a sequence of infinite cardinals where $δ< ω_3$ and $\ka_{\al}\in \{\om,λ\}$ for each $\al < δ$ in such a way that $f^{-1}\{\om\}$ is $\om_2$-closed in $δ$, then it is consistent that there is a scattered Boolean space whose cardinal sequence is $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A consistency theorem for cardinal sequences of length $< ω_3$ Martínez, Juan Carlos Soukup, Lajos Logic 03E35 We prove that if $λ$ is a fixed uncountable cardinal and $f = \langle \ka_{\al} : \al < δ\rangle$ is a sequence of infinite cardinals where $δ< ω_3$ and $\ka_{\al}\in \{\om,λ\}$ for each $\al < δ$ in such a way that $f^{-1}\{\om\}$ is $\om_2$-closed in $δ$, then it is consistent that there is a scattered Boolean space whose cardinal sequence is $f$. |
| title | A consistency theorem for cardinal sequences of length $< ω_3$ |
| topic | Logic 03E35 |
| url | https://arxiv.org/abs/2512.01418 |