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dc.contributor.authorFinkel, Olivieren
dc.contributor.authorTodorčević, Stevoen
dc.date.accessioned2020-05-01T20:29:24Z-
dc.date.available2020-05-01T20:29:24Z-
dc.date.issued2012-03-01en
dc.identifier.issn0022-4812en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2206-
dc.description.abstractWe consider ω n-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω n for some integer n ≥ 1. We show that all these structures are co-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω 2- automatic (resp. ω n-automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups) is not determined by the axiomatic system ZFC. We infer from the proof of the above result that the isomorphism problem for ω n-automatic boolean algebras, n ≥ 2, (respectively, rings, commutative rings, non commutative rings, non commutative groups) is neither a ∑ 12-set nor a π 12-set. We obtain that there exist infinitely many ω 2 -automatic, hence also ω-tree-automatic, atomless boolean algebras ℬ n, n ≥ 1, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorphic under an alternate axiom AT, strengthening a result of [14].en
dc.publisherCambridge University Press-
dc.relation.ispartofJournal of Symbolic Logicen
dc.subjectω-tree-automatic structures | ω -automatic structures n | Automata reading ordinal words | Boolean algebras | Groups | Independence results | Isomorphism relation | Models of set theory | Partial orders | Ringsen
dc.titleA hierarchy of tree-automatic structuresen
dc.typeArticleen
dc.identifier.doi10.2178/jsl/1327068708en
dc.identifier.scopus2-s2.0-84860124057en
dc.relation.firstpage350en
dc.relation.lastpage368en
dc.relation.issue1en
dc.relation.volume77en
dc.description.rankM21-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.grantfulltextnone-
crisitem.author.orcid0000-0003-4543-7962-
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