Fräıssé limits for infinite relational languages

We study Fräıssé limits for certain Fräıssé classes over infinite relational languages that behave similarly to those for finite languages. These include the Fräıssé classes of finite simplicial complexes, finite hypergraphs, and Sperner families on finite sets. With a natural choice of measure we show that almost all countable structures whose finite substructures lie in such a class are isomorphic to the Fräıssé limit, and a corresponding 0-1 law holds for finite models. In particular, we obtain a new 0-1 law for simplicial complexes, different from the previously known one due to Blass and Harary.