Ultrametric homogeneous structures

We shall present the theory of homogeneous Polish ultrametric structures. Our starting point is a Fraı̈ssé class of finite structures and the crucial tool is the universal homogeneous epimorphism. The new Fraı̈ssé limit is an inverse limit, nevertheless its universality is with respect to embeddings and, contrary to the Polish metric Fraı̈ssé theory of Ben Yaacov, homogeneity is strict, not approximate. We shall discuss some concrete examples. Joint work with C. Pech and M. Pech [https://arxiv.org/abs/2301.10953].