{"id":{"repo_id":"east-anglia","oai_identifier":"oai:ueaeprints.uea.ac.uk:56893"},"canonical_url":"https://search.dev.ndltd.org/etd/east-anglia/oai:ueaeprints.uea.ac.uk:56893","repository":{"repo_id":"east-anglia","name":"University of East Anglia","base_url":"https://ueaeprints.uea.ac.uk/cgi/oai2"},"display":{"title":"Better-Quasi-Orders: Extensions and Abstractions","abstract":"We generalise the notion of �-scattered to partial orders and prove that some large classes of �-scattered partial orders are better-quasi-ordered under embeddability. This generalises theorems of Laver, Corominas and Thomass�e regarding �-scattered linear orders, �-scattered trees, countable pseudo-trees and N-free partial orders. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satis�es a natural strengthening of better-quasi-order. We prove that some natural classes of structured �-scattered pseudo-trees are betterquasi- ordered, strengthening similar results of K�r���z, Corominas and Laver. We then use this theorem to prove that some large classes of graphs are better-quasi-ordered under the induced subgraph relation, thus generalising results of Damaschke and Thomass�e. We investigate abstract better-quasi-orders by modifying the normal de�nition of better-quasi-order to use an alternative Ramsey space rather than exclusively the Ellentuck space as is usual. We classify the possible notions of well-quasi-order that can arise by generalising in this way, before proving that the corresponding notion of better-quasi-order is closed under taking iterated power sets, as happens in the usual case. We consider Shelah's notion of better-quasi-orders for uncountable cardinals, and prove that the corresponding modi�cation of his de�nition using fronts instead of barriers is equivalent. This gives rise to a natural version of Simpson's de�nition of better-quasiorder for uncountable cardinals, even in the absence of any Ramsey-theoretic results. We give a classi�cation of the fronts on [�]!, providing a description of how far away a front is from being a barrier.","abstract_html":"We generalise the notion of �-scattered to partial orders and prove that some large classes of �-scattered partial orders are better-quasi-ordered under embeddability. This generalises theorems of Laver, Corominas and Thomass�e regarding �-scattered linear orders, �-scattered trees, countable pseudo-trees and N-free partial orders. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satis�es a natural strengthening of better-quasi-order. We prove that some natural classes of structured �-scattered pseudo-trees are betterquasi- ordered, strengthening similar results of K�r���z, Corominas and Laver. We then use this theorem to prove that some large classes of graphs are better-quasi-ordered under the induced subgraph relation, thus generalising results of Damaschke and Thomass�e. We investigate abstract better-quasi-orders by modifying the normal de�nition of better-quasi-order to use an alternative Ramsey space rather than exclusively the Ellentuck space as is usual. We classify the possible notions of well-quasi-order that can arise by generalising in this way, before proving that the corresponding notion of better-quasi-order is closed under taking iterated power sets, as happens in the usual case. We consider Shelah's notion of better-quasi-orders for uncountable cardinals, and prove that the corresponding modi�cation of his de�nition using fronts instead of barriers is equivalent. This gives rise to a natural version of Simpson's de�nition of better-quasiorder for uncountable cardinals, even in the absence of any Ramsey-theoretic results. We give a classi�cation of the fronts on [�]!, providing a description of how far away a front is from being a barrier.","abstract_has_math":false,"creators":["Mckay, Gregory"],"institution":"University of East Anglia","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-11","date_published":"2015-11","updated_at":"2026-07-24T02:12:13Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Mckay, Gregory"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-11"]},{"key":"dc:date.issued","label":"Date","values":["2015-11"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of East Anglia"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://ueaeprints.uea.ac.uk/id/eprint/56893/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://ueaeprints.uea.ac.uk/id/eprint/56893/1/Thesis_Gregory_McKay.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We generalise the notion of �-scattered to partial orders and prove that some large classes of �-scattered partial orders are better-quasi-ordered under embeddability. This generalises theorems of Laver, Corominas and Thomass�e regarding �-scattered linear orders, �-scattered trees, countable pseudo-trees and N-free partial orders. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satis�es a natural strengthening of better-quasi-order. We prove that some natural classes of structured �-scattered pseudo-trees are betterquasi- ordered, strengthening similar results of K�r���z, Corominas and Laver. We then use this theorem to prove that some large classes of graphs are better-quasi-ordered under the induced subgraph relation, thus generalising results of Damaschke and Thomass�e. We investigate abstract better-quasi-orders by modifying the normal de�nition of better-quasi-order to use an alternative Ramsey space rather than exclusively the Ellentuck space as is usual. We classify the possible notions of well-quasi-order that can arise by generalising in this way, before proving that the corresponding notion of better-quasi-order is closed under taking iterated power sets, as happens in the usual case. We consider Shelah's notion of better-quasi-orders for uncountable cardinals, and prove that the corresponding modi�cation of his de�nition using fronts instead of barriers is equivalent. This gives rise to a natural version of Simpson's de�nition of better-quasiorder for uncountable cardinals, even in the absence of any Ramsey-theoretic results. We give a classi�cation of the fronts on [�]!, providing a description of how far away a front is from being a barrier."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Better-Quasi-Orders: Extensions and Abstractions"]}]}],"canonical_facts":{"dc:creator":["Mckay, Gregory"],"dc:date":["2015-11"],"dc:date.issued":["2015-11"],"dc:description.abstract":["We generalise the notion of �-scattered to partial orders and prove that some large classes of �-scattered partial orders are better-quasi-ordered under embeddability. This generalises theorems of Laver, Corominas and Thomass�e regarding �-scattered linear orders, �-scattered trees, countable pseudo-trees and N-free partial orders. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satis�es a natural strengthening of better-quasi-order. We prove that some natural classes of structured �-scattered pseudo-trees are betterquasi- ordered, strengthening similar results of K�r���z, Corominas and Laver. We then use this theorem to prove that some large classes of graphs are better-quasi-ordered under the induced subgraph relation, thus generalising results of Damaschke and Thomass�e. We investigate abstract better-quasi-orders by modifying the normal de�nition of better-quasi-order to use an alternative Ramsey space rather than exclusively the Ellentuck space as is usual. We classify the possible notions of well-quasi-order that can arise by generalising in this way, before proving that the corresponding notion of better-quasi-order is closed under taking iterated power sets, as happens in the usual case. We consider Shelah's notion of better-quasi-orders for uncountable cardinals, and prove that the corresponding modi�cation of his de�nition using fronts instead of barriers is equivalent. This gives rise to a natural version of Simpson's de�nition of better-quasiorder for uncountable cardinals, even in the absence of any Ramsey-theoretic results. We give a classi�cation of the fronts on [�]!, providing a description of how far away a front is from being a barrier."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://ueaeprints.uea.ac.uk/id/eprint/56893/1/Thesis_Gregory_McKay.pdf"],"dc:language":["en"],"dc:publisher.department":["School of Mathematics"],"dc:publisher.institution":["University of East Anglia"],"dc:relation.isreferencedby":["https://ueaeprints.uea.ac.uk/id/eprint/56893/"],"dc:title":["Better-Quasi-Orders: Extensions and Abstractions"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T02:12:13Z"}