Between Whitehead groups and uniformization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914128222748672 |
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| author | Poór, Márk Shelah, Saharon |
| author_facet | Poór, Márk Shelah, Saharon |
| contents | For a given stationary set $S$ of countable ordinals we prove (in $\mathbf{ZFC}$) that the assertion "every $S$-ladder system has $\aleph_0$-uniformization" is equivalent to "every strongly $\aleph_1$-free abelian group of cardinality $\aleph_1$ with non-freeness invariant $\subseteq S$ is $\aleph_1$-coseparable, i.e. Ext$(G, \oplus_{i=0}^{\infty} \mathbb Z)=0$ (in particular Whitehead, i.e.\ Ext$(G, \mathbb Z)=0$)". This solves problems B3 and B4 from Eklof and Mekler's monograph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12585 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Between Whitehead groups and uniformization Poór, Márk Shelah, Saharon Logic Group Theory For a given stationary set $S$ of countable ordinals we prove (in $\mathbf{ZFC}$) that the assertion "every $S$-ladder system has $\aleph_0$-uniformization" is equivalent to "every strongly $\aleph_1$-free abelian group of cardinality $\aleph_1$ with non-freeness invariant $\subseteq S$ is $\aleph_1$-coseparable, i.e. Ext$(G, \oplus_{i=0}^{\infty} \mathbb Z)=0$ (in particular Whitehead, i.e.\ Ext$(G, \mathbb Z)=0$)". This solves problems B3 and B4 from Eklof and Mekler's monograph. |
| title | Between Whitehead groups and uniformization |
| topic | Logic Group Theory |
| url | https://arxiv.org/abs/2203.12585 |