Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914278424969216 |
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| author | Paolini, Gianluca Shelah, Saharon |
| author_facet | Paolini, Gianluca Shelah, Saharon |
| contents | In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable torsion-free abelian groups are faithfully Borel complete, in fact, more strongly, we can $\mathfrak{L}_{ω_1, ω}$-interpret countable graphs in them. Secondly, we show that the relation of pure embeddability (equiv., elementary embeddability) among countable models of $\mathrm{Th}(\mathbb{Z}^{(ω)})$ is a complete analytic quasi-order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04162 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order Paolini, Gianluca Shelah, Saharon Logic 03E15, 20K20 In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable torsion-free abelian groups are faithfully Borel complete, in fact, more strongly, we can $\mathfrak{L}_{ω_1, ω}$-interpret countable graphs in them. Secondly, we show that the relation of pure embeddability (equiv., elementary embeddability) among countable models of $\mathrm{Th}(\mathbb{Z}^{(ω)})$ is a complete analytic quasi-order. |
| title | Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order |
| topic | Logic 03E15, 20K20 |
| url | https://arxiv.org/abs/2312.04162 |