TMD is a new class of topological groups with tractable minimal dynamics, characterized by several equivalent conditions, equal to GPP on Polish groups, admitting an abstract KPT correspondence, and yielding a forcing-based proof of the revised Newelski conjecture for all definable NIP groups.
Extremely amenable groups via continuous logic
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abstract
We establish a characterization of extreme amenability of any Polish group in Fra\"iss\'e-theoretic terms in the setting of continuous logic, mirroring a theorem due to Kechris, Pestov and Todorcevic for closed subgroups of the permutation group of an infinite countable set.
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Topological groups with tractable minimal dynamics
TMD is a new class of topological groups with tractable minimal dynamics, characterized by several equivalent conditions, equal to GPP on Polish groups, admitting an abstract KPT correspondence, and yielding a forcing-based proof of the revised Newelski conjecture for all definable NIP groups.