Year: 2017
Type: preprint
Abstract: We prove that the Fraïssé limit of a Fraïssé 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 $p$.
Source: arXiv (Cornell University)
Authors: Kabluchko, Zakhar, Tent, Katrin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2765958561