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.
Games with finitely generated structures
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abstract
We study the abstract Banach-Mazur game played with finitely generated structures instead of open sets. We characterize the existence of winning strategies aiming at a single countably generated structure. We also introduce the concept of weak Fraisse classes, extending the classical Fraisse theory and revealing its relations to our Banach-Mazur game.
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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.