On countable isotypic structures
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912433994465280 |
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| author | Gvozdevsky, Pavel |
| author_facet | Gvozdevsky, Pavel |
| contents | We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with countable underlying sets: totally ordered sets, fields, and groups. This answers an old question by B. Plotkin for groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10812 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On countable isotypic structures Gvozdevsky, Pavel Logic 03C07(Primary) 03C60, 03C64 and 12L12(Secondary) We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with countable underlying sets: totally ordered sets, fields, and groups. This answers an old question by B. Plotkin for groups. |
| title | On countable isotypic structures |
| topic | Logic 03C07(Primary) 03C60, 03C64 and 12L12(Secondary) |
| url | https://arxiv.org/abs/2308.10812 |