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arXiv · 2308.10812

On countable isotypic structures

Pavel Gvozdevsky
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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.

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Pavel Gvozdevsky. 2023-08-21. On countable isotypic structures. https://doi.org/10.46298/jgcc.2024.16.1.13493

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