Coxeter Groups and Abstract Elementary Classes : The Right-Angled Case

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dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor.author Hyttinen, Tapani
dc.contributor.author Paolini, Gianluca
dc.date.accessioned 2019-11-25T14:15:01Z
dc.date.available 2019-11-25T14:15:01Z
dc.date.issued 2019-11
dc.identifier.citation Hyttinen , T & Paolini , G 2019 , ' Coxeter Groups and Abstract Elementary Classes : The Right-Angled Case ' , Notre Dame Journal of Formal Logic , vol. 60 , no. 4 , pp. 707-731 . https://doi.org/10.1215/00294527-2019-0027 en
dc.identifier.issn 0029-4527
dc.identifier.other PURE: 127911160
dc.identifier.other PURE UUID: dd5b9ad9-f435-4ceb-ba1d-b00b49a55b91
dc.identifier.other WOS: 000491225400008
dc.identifier.other ORCID: /0000-0002-5125-3839/work/64325812
dc.identifier.uri http://hdl.handle.net/10138/307407
dc.description.abstract We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single L-omega 1,L- omega-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is kappa-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph. en
dc.format.extent 25
dc.language.iso eng
dc.relation.ispartof Notre Dame Journal of Formal Logic
dc.rights en
dc.subject classification theory en
dc.subject abstract elementary classes en
dc.subject Coxeter groups en
dc.subject AUTOMORPHISMS en
dc.subject RIGIDITY en
dc.subject 111 Mathematics en
dc.title Coxeter Groups and Abstract Elementary Classes : The Right-Angled Case en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.1215/00294527-2019-0027
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/acceptedVersion
dc.contributor.pbl

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