A generalization of Kechris-Rosendal characterizes comeager diagonal conjugacy classes in arbitrary Polish permutation groups, and ball-preserving groups of ordered ultrametric spaces are shown to have a generic element but no generic pair.
Examples of weak amalgamation classes
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abstract
We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamation property. These include a continuum-sized family of classes of finite undirected graphs, as well as an example due to Pouzet with countably categorical generic limit.
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math.LO 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups
A generalization of Kechris-Rosendal characterizes comeager diagonal conjugacy classes in arbitrary Polish permutation groups, and ball-preserving groups of ordered ultrametric spaces are shown to have a generic element but no generic pair.