Reducts of random hypergraphs
type: Item
instance of: scholarly article
title: Reducts of random hypergraphs
zbMATH Open document ID: 0865.03025
DOI: 10.1016/0168-0072(95)00061-5
author: Simon Thomas
published in: Annals of Pure and Applied Logic
publication date: 1997-07-01T00:00:00Z
full work available at URL: http://hdl.handle.net/11693/49063
review text: Let \(M\) be a countable \(\omega\)-categorical structure on a set \(A\). The structure \(N=\langle A,R_0,\dots,R_\alpha,\dots\rangle\) is said to be a reduct of \(M\) iff every \(R_\alpha\) is definable without parameters in \(M\). For any closed permutation group \(G\) the condition \((*):\text{Aut}(M) \leq G\leq \text{Sym}(A)\) (where \(\text{Sym}(A)\) is the group of all permutations of \(A\)) is equivalent to \(G=\text{Aut}(N)\) for some reduct \(N\) of \(M\). Reducts \(N_1\) and \(N_2\) of \(M\) are said to be equivalent iff each is a reduct of the other, i.e. iff \(\text{Aut }N_1=\text{Aut }N_2\). Thus the problem of classifying the reducts of \(M\) up to equivalence is the same as that of classifying the closed permutation groups \(G\) satisfying \((*)\). The author gives the classification of the closed permutation groups \(G\) satisfying \((*)\) for the universal homogeneous \(k\)-hypergraphs \(M\).
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 03C65
Mathematics Subject Classification ID: 22A25
zbMATH DE Number: 933086
zbMATH Keywords: equivalent reducts
zbMATH Keywords: classification of reducts
zbMATH Keywords: random hypergraphs
zbMATH Keywords: automorphism groups
zbMATH Keywords: countable \(\omega\)-categorical structure
zbMATH Keywords: reduct
zbMATH Keywords: permutation groups
zbMATH Keywords: universal homogeneous \(k\)-hypergraphs
MaRDI profile type: Publication
OpenAlex ID: W2157624263
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description: scientific article; zbMATH DE number 933086