Ultrahomogeneous structures: some infinite examples
by
Alice Devillers
ULB Bruxelles BELGIUM

Given a positive integer d, a relational structure S is said to be d-ultrahomogeneous if every isomorphism between two substructures of S of cardinality at most d can be extended into an automorphism of S. S is said to be ultrahomogeneous if it is d-ultrahomogeneous for every positive integer d.

In this talk, we will describe several examples of infinite (d)-ultrahomogeneous structures.

The famous random graph discovered in 1963 by Erdös and Rényi turns out to be ultrahomogeneous.

The classification of infinite 4-ultrahomogeneous linear spaces leads to the study of infinite projective planes having remarkable properties (one of these planes is Desarguesian and is obtained from a special skew field constructed in 1977 by Cohn, but there are at least countably many non-Desarguesian ones, related to model theory).

We will also describe two infinite families of ultrahomogeneous semilinear spaces, whose number of points is any given cardinal number.

Adress of the author:

Université Libre de Bruxelles
Département de Mathématiques - C.P.216
Boulevard du Triomphe
B-1050 Brussels, Belgium

Date received: February 12, 2001