Submission date: 25 NOvember 2017

Abstract:

Using the natural action of S_∞ we show that a countable hereditary class C of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a structure M whose isomorphism type is comeager in the space of all countable, infinitely generated structures with age in C. In this case, M is the weak Fraïssé limit of C.
This applies in particular to countable structures with generic automorphisms and recovers a result by Kechris and Rosendal [Proc. Lond. Math. Soc., 2007].

Mathematics Subject Classification: 03C15, Secondary: 54E52, 60B99, 22F50

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Full text arXiv 1711.09295: pdf, ps.