Pavel Gvozdevsky - On countable isotypic structures
gcc:13493 - journal of Groups, complexity, cryptology, May 14, 2024, Volume 16, Issue 1, Special issue in memory of Ben Fine - https://doi.org/10.46298/jgcc.2024.16.1.13493On countable isotypic structuresArticle
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.
Comment: 6 pages, Published in journal of Groups, Complexity, Cryptology
Source: arXiv.org:2308.10812
Volume: Volume 16, Issue 1, Special issue in memory of Ben Fine
Published on: May 14, 2024
Submitted on: April 30, 2024
Keywords: Mathematics - Logic, 03C07(Primary) 03C60, 03C64 and 12L12(Secondary)
Classifications
Mathematics Subject Classification 20201
1 Document citing this article
Consultation statistics
This page has been seen 2221 times.
This article's PDF has been downloaded 1769 times.