Uniform local weak o-minimality and $*$-local weak o-minimality
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_ | 1866917662628511744 |
|---|---|
| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | We propose the notions of uniform local weak o-minimality and $*$-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In this paper, we demonstrate new local monotonicity theorems for uniformly locally weakly o-minimal structures of the second kind and for locally o-minimal structures under the assumption called the univariate $*$-continuity property. We also prove that several formulas for dimension of definable sets which hold in definably complete locally o-minimal structures also hold in $*$-locally weakly o-minimal structures possessing the univariate $*$-continuity property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform local weak o-minimality and $*$-local weak o-minimality Fujita, Masato Logic 03C64 We propose the notions of uniform local weak o-minimality and $*$-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In this paper, we demonstrate new local monotonicity theorems for uniformly locally weakly o-minimal structures of the second kind and for locally o-minimal structures under the assumption called the univariate $*$-continuity property. We also prove that several formulas for dimension of definable sets which hold in definably complete locally o-minimal structures also hold in $*$-locally weakly o-minimal structures possessing the univariate $*$-continuity property. |
| title | Uniform local weak o-minimality and $*$-local weak o-minimality |
| topic | Logic 03C64 |
| url | https://arxiv.org/abs/2405.06140 |