Universal-homogeneous structures are generic

Zakhar Kabluchko; Katrin Tent

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arXiv · 1710.06137

Universal-homogeneous structures are generic

Zakhar Kabluchko·Katrin Tent

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Abstract

We prove that the Fra\"iss\'e limit of a Fra\"iss\'e class $\mathcal C$ is the (unique) countable structure whose isomorphism type is comeager (with respect to a certain logic topology) in the Baire space of all structures whose age is contained in $\mathcal C$ and which are defined on a fixed countable universe. In particular, the set of groups isomorphic to Hall's universal group is comeager in the space of all countable locally finite groups and the set of fields isomorphic to the algebraic closure of $\mathbb F_p$ is comeager in the space of countable fields of characteristic $p$.

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BibTeX RIS

Zakhar Kabluchko, Katrin Tent. 2017-10-17. Universal-homogeneous structures are generic. https://arxiv.org/abs/1710.06137

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