On countable isotypic structures
Logic
2025-06-18 v4
Abstract
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.
Keywords
Cite
@article{arxiv.2308.10812,
title = {On countable isotypic structures},
author = {Pavel Gvozdevsky},
journal= {arXiv preprint arXiv:2308.10812},
year = {2025}
}
Comments
6 pages, Published in journal of Groups, Complexity, Cryptology