Pseudo T-closed fields
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929422430371840 |
|---|---|
| author | Montenegro, Samaria Rideau-Kikuchi, Silvain |
| author_facet | Montenegro, Samaria Rideau-Kikuchi, Silvain |
| contents | Pseudo algebraically closed, pseudo real closed, and pseudo $p$-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for studying them: the class of pseudo $T$-closed fields, where $T$ is an enriched theory of fields. These fields verify a "local-global" principle for the existence of points on varieties with respect to models of $T$. This approach also enables a good description of some fields equipped with multiple $V$-topologies, particularly pseudo algebraically closed fields with a finite number of valuations. One important result is a (model theoretic) classification result for bounded pseudo $T$-closed fields, in particular we show that under specific hypotheses on $T$, these fields are NTP$_2$ of finite burden. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10433 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pseudo T-closed fields Montenegro, Samaria Rideau-Kikuchi, Silvain Logic Pseudo algebraically closed, pseudo real closed, and pseudo $p$-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for studying them: the class of pseudo $T$-closed fields, where $T$ is an enriched theory of fields. These fields verify a "local-global" principle for the existence of points on varieties with respect to models of $T$. This approach also enables a good description of some fields equipped with multiple $V$-topologies, particularly pseudo algebraically closed fields with a finite number of valuations. One important result is a (model theoretic) classification result for bounded pseudo $T$-closed fields, in particular we show that under specific hypotheses on $T$, these fields are NTP$_2$ of finite burden. |
| title | Pseudo T-closed fields |
| topic | Logic |
| url | https://arxiv.org/abs/2304.10433 |