Reducts of the Generic Digraph

2014/11/18 by Lovkush Agarwal, Agarwal, Lovkush · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #math.CO #math.LO

paper · pdf · doi:10.48550/arxiv.1411.4820

arxiv created 2014/11/18 · arxiv updated 2014/11/19

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 M is a reduct of (D,E) if it has domain D and all its ∅-definable relations are ∅-definable relations of (D,E). As (D,E) is ℵ₀-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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