An uncountable analogue of Fraïssé's theorem.

Title: An uncountable analogue of Fraïssé's theorem.

Abstract:  Given a suitable class K of finite structures, a theorem of Fraïssé shows how to construct a special model, called the Fraïssé limit of K: the unique strongly homogeneous countable structure whose finite substructures are precisely the members of K. Some classes of finite structures do not satisfy the hypotheses of Fraïssé’s theorem, and therefore do not have Fraïssé limits. In some cases, however, there is nevertheless a special model of size c, which looks remarkably like a Fraïssé limit except that it has a larger cardinality. We will describe these structures and their similarity to Fraïssé limits, and give one or two examples of familiar structures that can be realized in this way.