2010 seminar talk: Fraïssé limits for a kind of "locally finite" Fraïssé class
Talk held by Andrew Brooke-Taylor (Bristol University and the Heilbronn Institute for Mathematical Research) at the KGRC seminar on 2010-05-20.
One of the nicest results about Fraïssé limits is the fact that, when the language is finite, one obtains a 0-1 law for members of the Fraïssé class. We introduce a notion of locally finite Fraïssé class, for which the language is infinite, but the Fraïssé class acts like one for a finite language. Examples include the Fraïssé classes of finite hypergraphs, finite simplicial complexes, and antichains on P(n) for finite n. Amongst other results, we derive a 0-1 law for such structures; notably, ours differs from the known 0-1 law for simplicial complexes of Blass & Harary, as we use a different by still very natural choice of measure guided by the Fraïssé limit considerations.