Automorphisms and strongly invariant relations

We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A = ω 1 , we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary int...

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Bibliographic Details
Published in:Algebra universalis 2023-11, Vol.84 (4), Article 27
Main Authors: Börner, Ferdinand, Goldstern, Martin, Shelah, Saharon
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Invariants
Mathematics
Mathematics and Statistics
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Summary:We investigate characterizations of the Galois connection Aut - sInv between sets of finitary relations on a base set A and their automorphisms. In particular, for A = ω 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 ω -categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-023-00818-4