The weak Ramsey property and extreme amenability

Adam Bartoš, Tristan Bice, Keegan Dasilva Barbosa, Wiesław Kubiś

Published 2021-10-04, updated 2024-08-26Version 2

We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples including monoid categories, the category of almost linear orders, and categories of strong embeddings of trees.