Isomorphism types of definable (maximal) cofinitary groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911347163267072 |
|---|---|
| author | Schembecker, Lukas |
| author_facet | Schembecker, Lukas |
| contents | Kastermans proved that consistently $\bigoplus_{\aleph_1} \mathbb{Z}_2$ has a cofinitary representation. We present a short proof that $\bigoplus_{\mathfrak{c}} \mathbb{Z}_2$ always has an arithmetic cofinitary representation. Further, for every finite group $F$ we construct an arithmetic maximal cofinitary group of isomorphism type $(\ast_{\mathfrak{c}} \mathbb{Z}) \times F$. This answers an implicit question by Schrittesser and Mejak whether one may construct definable maximal cofinitary groups not decomposing into free products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphism types of definable (maximal) cofinitary groups Schembecker, Lukas Logic Kastermans proved that consistently $\bigoplus_{\aleph_1} \mathbb{Z}_2$ has a cofinitary representation. We present a short proof that $\bigoplus_{\mathfrak{c}} \mathbb{Z}_2$ always has an arithmetic cofinitary representation. Further, for every finite group $F$ we construct an arithmetic maximal cofinitary group of isomorphism type $(\ast_{\mathfrak{c}} \mathbb{Z}) \times F$. This answers an implicit question by Schrittesser and Mejak whether one may construct definable maximal cofinitary groups not decomposing into free products. |
| title | Isomorphism types of definable (maximal) cofinitary groups |
| topic | Logic |
| url | https://arxiv.org/abs/2512.24318 |