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Preprint Number 1320

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1320. Zakhar Kabluchko and Katrin Tent
Universal-homogeneous structures are generic
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Submission date: 17 October 2017

Abstract:

We prove that the Fraïssé limit of a Fraïssé class 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 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 F_p is comeager in the space of countable fields of characteristic p.

Mathematics Subject Classification: Primary: 03C15, Secondary: 54E52, 60B99

Keywords and phrases:

Full text arXiv 1710.06137: pdf, ps.


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