Preservation of NATP
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929454427668480 |
|---|---|
| author | Ahn, JinHoo Kim, Joonhee Lee, Hyoyoon Lee, Junguk |
| author_facet | Ahn, JinHoo Kim, Joonhee Lee, Hyoyoon Lee, Junguk |
| contents | We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces. Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP$_1$ and NTP$_2$ are considered. Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08753 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Preservation of NATP Ahn, JinHoo Kim, Joonhee Lee, Hyoyoon Lee, Junguk Logic 03C45, 03C60 We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces. Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP$_1$ and NTP$_2$ are considered. Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP. |
| title | Preservation of NATP |
| topic | Logic 03C45, 03C60 |
| url | https://arxiv.org/abs/2209.08753 |