Generic groups and the weak amalgamation property
Logic
2025-12-03 v3 Group Theory
Abstract
We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.
Cite
@article{arxiv.2402.02143,
title = {Generic groups and the weak amalgamation property},
author = {Aleksander Ivanov and Krzysztof Majcher},
journal= {arXiv preprint arXiv:2402.02143},
year = {2025}
}
Comments
In the third arxiv version of the paper we generalize the definition of t-isolation. As a result Proposition 3.1 and Theorems 3.2 are given in a form which unifies the cases of groups, semigroups and rings. There are some additional discussions and remarks. Now the length of the paper is 21 pages