Existentially closed models and locally zero-dimensional toposes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929374514642944 |
|---|---|
| author | Kamsma, Mark Wrigley, Joshua |
| author_facet | Kamsma, Mark Wrigley, Joshua |
| contents | The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as the fact that every model admits a homomorphism to an existentially closed one. Other properties do not generalise: classically, there are two equivalent definitions of an existentially closed model, but this equivalence breaks down for the generalised notion. We study the interaction of these two conditions on the topos-theoretic level, and characterise the classifying topos of the e.c. geometric morphisms when the conditions coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02788 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existentially closed models and locally zero-dimensional toposes Kamsma, Mark Wrigley, Joshua Category Theory Logic 03G30 (primary) 03B20, 03B22, 18B25, 18C10 (secondary) The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as the fact that every model admits a homomorphism to an existentially closed one. Other properties do not generalise: classically, there are two equivalent definitions of an existentially closed model, but this equivalence breaks down for the generalised notion. We study the interaction of these two conditions on the topos-theoretic level, and characterise the classifying topos of the e.c. geometric morphisms when the conditions coincide. |
| title | Existentially closed models and locally zero-dimensional toposes |
| topic | Category Theory Logic 03G30 (primary) 03B20, 03B22, 18B25, 18C10 (secondary) |
| url | https://arxiv.org/abs/2406.02788 |