Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings
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?
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
Publication
Order
Status
Peer reviewed
ISSN
0167-8094Type
Journal article
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.