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Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings
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dc.contributor.author | Ironmonger, Victoria Louise | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2024-02-21T16:30:15Z | |
dc.date.available | 2024-02-21T16:30:15Z | |
dc.date.issued | 2024-02-14 | |
dc.identifier | 298462043 | |
dc.identifier | 0ff8b5fd-6cfe-4212-93da-b90a6a913ea0 | |
dc.identifier | 85185116499 | |
dc.identifier.citation | Ironmonger , V L & Ruskuc , N 2024 , ' Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings ' , Order . https://doi.org/10.1007/s11083-024-09659-9 | en |
dc.identifier.issn | 0167-8094 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/153977339 | |
dc.identifier.uri | https://hdl.handle.net/10023/29315 | |
dc.description.abstract | We consider the posets of equivalence relations on finite sets under the standard embedding ordering and under the consecutive embedding ordering. In the latter case, the relations are also assumed to have an underlying linear order, which governs consecutive embeddings. For each poset we ask the well quasi-order and atomicity decidability questions: Given finitely many equivalence relations ρ1,...,ρk, is the downward closed set Av(ρ1,...,ρk) consisting of all equivalence relations which do not contain any of ρ1,...,ρk (a) well-quasi-ordered, meaning that it contains no infinite antichains? and (b) atomic, meaning that it is not a union of two proper downward closed subsets, or, equivalently, that it satisfies the joint embedding property? | |
dc.format.extent | 26 | |
dc.format.extent | 727794 | |
dc.language.iso | eng | |
dc.relation.ispartof | Order | en |
dc.subject | Equivalence relation | en |
dc.subject | Embedding | en |
dc.subject | Poset | en |
dc.subject | Well quasi-order | en |
dc.subject | Antichain | en |
dc.subject | Atomic | en |
dc.subject | Joint embedding property | en |
dc.subject | Graph | en |
dc.subject | Path | en |
dc.subject | Subpath | en |
dc.subject | Decidability | en |
dc.subject | QA Mathematics | en |
dc.subject | T-DAS | en |
dc.subject.lcc | QA | en |
dc.title | Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1007/s11083-024-09659-9 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/2301.11048 | en |
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