2015/09/25 by Lovkush Agarwal, Agarwal, Lovkush, Michael Kompatscher +1 · 1 citation
Mathematics · #03C99 #05E18 (Primary) #20B27 #20B35 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Logic (math.LO) #math.CO #math.GR #math.LO #msc:03C99 #msc:05E18 #msc:20B27 #msc:20B35
paper · pdf · doi:10.48550/arxiv.1509.07674
arxiv created 2015/09/25 · openalex publication_date 2015/09/25 · arxiv updated 2015/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given two structures M and N on the same domain, we say that N is a reduct of M if all ∅-definable relations of N are ∅-definable in M. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are ℵ0-categorical, determining their reducts is equivalent to determining all closed supergroups G< Sym(ℕ) of their automorphism groups. A consequence of the classification is that there are 2ℵ0 pairwise non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are 2ℵ0 pairwise non-conjugate maximal-closed subgroups of Sym(ℕ). By the reconstruction results of Rubin, these groups are also non-isomorphic as abstract groups.