Automorphisms and strongly invariant relations

Ferdinand Börner; Martin Goldstern; Saharon Shelah

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arXiv · math/0309165

Automorphisms and strongly invariant relations

Ferdinand Börner·Martin Goldstern·Saharon Shelah

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Abstract

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 closed under all invariant operations on relations and under arbitray 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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BibTeX RIS

Ferdinand Börner, Martin Goldstern, Saharon Shelah. 2003-09-09. Automorphisms and strongly invariant relations. https://arxiv.org/abs/math/0309165

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