# 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.

• Current version: 2005-12-03_11 (20p)
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}
}