The weak Ramsey property and extreme amenability

Abstract

We extend the Kechris–Pestov–Todorčević correspondence to weak Fraïssé 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.

Keywords

• 05C55
• 22F50
• 05D10
• 18A30
• 54H11