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arXiv · 2210.06899

Projective Fra\"{i}ss\'{e} limits and generalized Wa\.{z}ewski dendrites

Alessandro Codenotti·Aleksandra Kwiatkowska
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Abstract

We continue the study of projective Fra\"{i}ss\'{e} limits of trees initiated by Charatonik and Roe and we construct many generalized Wa\.{z}ewski dendrites as the topological realization of a projective Fra\"{i}ss\'{e} limit of families of finite trees with (weakly) coherent epimorphisms. Moreover we use the categorical approach to Fra\"{i}ss\'{e} limits developed by Kubi\'{s} to construct all generalized Wa\.{z}ewski dendrites as topological realizations of Fra\"{i}ss\'{e} limits of suitable categories of finite structures. As an application we recover a homogeneity result for countable dense sets of endpoints in generalized Wa\.{z}ewski dendrites.

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Alessandro Codenotti, Aleksandra Kwiatkowska. 2022-10-13. Projective Fra\"{i}ss\'{e} limits and generalized Wa\.{z}ewski dendrites. https://arxiv.org/abs/2210.06899

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