%0 Journal Article %T Automorphisms and strongly invariant relations %A Ferdinand B£¿rner %A Martin Goldstern %A Saharon Shelah %J Mathematics %D 2003 %I arXiv %X We investigate characterizations of the Galois connection sInv-Aut between sets of finitary relations on a base set A and their automorphisms. In particular, for A=omega_1, we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitray intersections, but is not closed under sInv(Aut(-)). Our structure (A,R) has an omega-categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous. %U http://arxiv.org/abs/math/0309165v1