Automorphisms and strongly invariant relations

by Boerner and Goldstern and Shelah. [BGSh:822]

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 arbitrary 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.

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