# Sh:822

- Börner, F., Goldstern, M., & Shelah, S. (2023).
*Automorphisms and strongly invariant relations*. Algebra Universalis,**84**(4), Paper No. 27, 23. arXiv: math/0309165 DOI: 10.1007/s00012-023-00818-4 MR: 4629461 -
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.

- Version 2023-04-23_2 (21p)

Bib entry

@article{Sh:822, author = {B{\"o}rner, Ferdinand and Goldstern, Martin and Shelah, Saharon}, title = {{Automorphisms and strongly invariant relations}}, journal = {Algebra Universalis}, fjournal = {Algebra Universalis}, volume = {84}, number = {4}, year = {2023}, pages = {Paper No. 27, 23}, issn = {0002-5240}, mrnumber = {4629461}, mrclass = {03C50 (03C10 06A15)}, doi = {10.1007/s00012-023-00818-4}, note = {\href{https://arxiv.org/abs/math/0309165}{arXiv: math/0309165}}, arxiv_number = {math/0309165} }