The generic countable lattice
by
Martin Goldstern
TU Wien

Fix a countable set X. There is a natural topology on the set L(X) of lattices with underlying set X, making L(X) into a complete metric space.

The meager (=first category) subsets of L(X) form a proper sigma-ideal; we will say that a property P is true for "almost all countable lattices" if the set of lattices without P is a meager set.

I will show that there is a countable lattice L* such that almost all countable lattices are isomorphic to it, and I will investigate some basic properties of L*.

As a consequence, we will see that "almost all" countable lattices are (for example) locally finite, and have the interpolation property (as far as monotone functions are concerned).

Date received: January 25, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caht-11.