2017/11/25 by Kabluchko, Zakhar, Tent, Katrin
#03C15 #22F50 #60B99 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Secondary: 54E52
paper · doi:10.48550/arxiv.1711.09295
Using the natural action of S_∞ we show that a countable hereditary class \mathcal 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 \mathcal C. In this case, M is the weak Fraïssé limit of \mathcal C. This applies in particular to countable structures with generic automorphisms and recovers a result by Kechris and Rosendal [Proc. Lond. Math. Soc., 2007].