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
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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