Which Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set?
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910565611339776 |
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| author | Karagila, Asaf Ryan-Smith, Calliope |
| author_facet | Karagila, Asaf Ryan-Smith, Calliope |
| contents | Given any $λ\leqκ$, we construct a symmetric extension in which there is a set $X$ such that $\aleph(X)=λ$ and $\aleph^*(X)=κ$. Consequently, we show that $\mathsf{ZF}+$"For all pairs of infinite cardinals $λ\leqκ$ there is a set $X$ such that $\aleph(X)=λ\leqκ=\aleph^*(X)$" is consistent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11409 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Which Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set? Karagila, Asaf Ryan-Smith, Calliope Logic 03E25 (Primary) 03E35 (Secondary) Given any $λ\leqκ$, we construct a symmetric extension in which there is a set $X$ such that $\aleph(X)=λ$ and $\aleph^*(X)=κ$. Consequently, we show that $\mathsf{ZF}+$"For all pairs of infinite cardinals $λ\leqκ$ there is a set $X$ such that $\aleph(X)=λ\leqκ=\aleph^*(X)$" is consistent. |
| title | Which Pairs of Cardinals Can Be Hartogs and Lindenbaum Numbers of a Set? |
| topic | Logic 03E25 (Primary) 03E35 (Secondary) |
| url | https://arxiv.org/abs/2309.11409 |