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arXiv · 1411.4820

Reducts of the Generic Digraph

Lovkush Agarwal
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Abstract

The generic digraph $(D,E)$ is the unique countable homogeneous digraph that embeds all finite digraphs. In this paper, we determine the lattice of reducts of $(D,E)$, where a structure $\mathcal{M}$ is a reduct of $(D,E)$ if it has domain $D$ and all its $\emptyset$-definable relations are $\emptyset$-definable relations of $(D,E)$. As $(D,E)$ is $\aleph_0$-categorical, this is equivalent to determining the lattice of closed groups that lie in between Aut$(D,E)$ and Sym$(D)$.

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Lovkush Agarwal. 2014-11-18. Reducts of the Generic Digraph. https://arxiv.org/abs/1411.4820

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