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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.09989 |
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| _version_ | 1866911551587352576 |
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| author | Hils, Martin Liccardo, Martina Touchard, Pierre |
| author_facet | Hils, Martin Liccardo, Martina Touchard, Pierre |
| contents | We investigate when an ordered abelian group $G$ is stably embedded in a given elementary extension $H$. We focus on a large class of ordered groups which includes maximal ordered groups with interpretable archimedean valuation. We give a complete answer for groups in this class which takes the form of a transfer principle for valued groups. It follows in particular that all types in the lexicographic product $\prod_{i\in ω} \mathbb{Z}$ are definable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09989 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stably Embedded Pairs of Ordered Abelian Groups Hils, Martin Liccardo, Martina Touchard, Pierre Logic We investigate when an ordered abelian group $G$ is stably embedded in a given elementary extension $H$. We focus on a large class of ordered groups which includes maximal ordered groups with interpretable archimedean valuation. We give a complete answer for groups in this class which takes the form of a transfer principle for valued groups. It follows in particular that all types in the lexicographic product $\prod_{i\in ω} \mathbb{Z}$ are definable. |
| title | Stably Embedded Pairs of Ordered Abelian Groups |
| topic | Logic |
| url | https://arxiv.org/abs/2308.09989 |