The weak Ramsey property is a variant of the finite Ramsey property, used for characterizing extreme amenability of automorphism groups of ultra-homogeneous structures, known as the Kechris - Pestov - Todorcevic correspondence. We shall describe a far reaching extension of the KPT correspondence, indicating also how it works in metric-enriched categories, capturing objects from topology and functional analysis.
Joint work with A. Bartos, T. Bice, and K. Dasilva Barbosa.
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