Countable Ordered Groups and Weihrauch Reducibility
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908402578358272 |
|---|---|
| author | Li, Ang |
| author_facet | Li, Ang |
| contents | This paper continues to study the connection between reverse mathematics and Weihrauch reducibility. In particular, we study the problems formed from Maltsev's theorem on the order types of countable ordered groups. Solomon showed that the theorem is equivalent to $\mathsf{Π_1^1}$-$\mathsf{CA_0}$, the strongest of the big five subsystems of second order arithmetic. We show that the strength of the theorem comes from having a dense linear order without endpoints in its order type. Then, we show that for the related Weihrauch problem to be strong enough to be equivalent to $\mathsf{\hat{WF}}$ (the analog problem of $\mathsf{Π_1^1}$-$\mathsf{CA_0}$), an order-preserving function is necessary in the output. Without the order-preserving function, the problems are very much to the side compared to analog problems of the big five. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Countable Ordered Groups and Weihrauch Reducibility Li, Ang Logic Group Theory 03D78, 03D30, 06F15, 03B30 This paper continues to study the connection between reverse mathematics and Weihrauch reducibility. In particular, we study the problems formed from Maltsev's theorem on the order types of countable ordered groups. Solomon showed that the theorem is equivalent to $\mathsf{Π_1^1}$-$\mathsf{CA_0}$, the strongest of the big five subsystems of second order arithmetic. We show that the strength of the theorem comes from having a dense linear order without endpoints in its order type. Then, we show that for the related Weihrauch problem to be strong enough to be equivalent to $\mathsf{\hat{WF}}$ (the analog problem of $\mathsf{Π_1^1}$-$\mathsf{CA_0}$), an order-preserving function is necessary in the output. Without the order-preserving function, the problems are very much to the side compared to analog problems of the big five. |
| title | Countable Ordered Groups and Weihrauch Reducibility |
| topic | Logic Group Theory 03D78, 03D30, 06F15, 03B30 |
| url | https://arxiv.org/abs/2409.19229 |