Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28483 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908921217679360 |
|---|---|
| author | Boissonneau, Blaise Stout, Mathias Vermeulen, Floris |
| author_facet | Boissonneau, Blaise Stout, Mathias Vermeulen, Floris |
| contents | We consider the model-theoretic Grothendieck ring of definable sets in ordered abelian groups. It is well-known that $\mathrm{K} \mathbb{Q} \cong \mathbb{Z}[T]/(T^2 + T)$ and $\mathrm{K} \mathbb{Z} =0$, but surprisingly little is known about other cases. We present a short computation which shows that they all collapse: $\mathrm{K} G = 0$, unless $G$ is divisible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28483 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Grothendieck ring of a non-divisible ordered abelian group is trivial Boissonneau, Blaise Stout, Mathias Vermeulen, Floris Logic We consider the model-theoretic Grothendieck ring of definable sets in ordered abelian groups. It is well-known that $\mathrm{K} \mathbb{Q} \cong \mathbb{Z}[T]/(T^2 + T)$ and $\mathrm{K} \mathbb{Z} =0$, but surprisingly little is known about other cases. We present a short computation which shows that they all collapse: $\mathrm{K} G = 0$, unless $G$ is divisible. |
| title | The Grothendieck ring of a non-divisible ordered abelian group is trivial |
| topic | Logic |
| url | https://arxiv.org/abs/2603.28483 |