Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups
Logic
2022-03-11 v3 Group Theory
Abstract
We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure , Polish group of permutations of , and , has a comeager -diagonal conjugacy class iff the family of all -tuples of -extendable bijections between finitely generated substructures of , has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fra\"{i}ss\'{e} classes that are not homogenizable. Finally, we investigate - and -diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.
Cite
@article{arxiv.1908.09494,
title = {Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups},
author = {Maciej Malicki},
journal= {arXiv preprint arXiv:1908.09494},
year = {2022}
}