Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups

Maciej Malicki

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arXiv · 1908.09494

Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups

Maciej Malicki

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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 $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$, $G$ has a comeager $n$-diagonal conjugacy class iff the family of all $n$-tuples of $G$-extendable bijections between finitely generated substructures of $M$, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. Finally, we investigate $1$- and $2$-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.

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BibTeX RIS

Maciej Malicki. 2022-03-10. Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups. https://arxiv.org/abs/1908.09494

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