# Sh:822

- Börner, F., Goldstern, M., & Shelah, S.
*Automorphisms and strongly invariant relations*. Preprint. arXiv: math/0309165 -
Abstract:

We investigate characterizations of the Galois connection {\rm sInv}–{\rm 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 {\rm sInv}{\rm 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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Bib entry

@article{Sh:822, author = {B{\"o}rner, Ferdinand and Goldstern, Martin and Shelah, Saharon}, title = {{Automorphisms and strongly invariant relations}}, note = {\href{https://arxiv.org/abs/math/0309165}{arXiv: math/0309165}}, arxiv_number = {math/0309165}, ignore = {x} }