@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Moconja, Slavko"@en ; dcterms:issued "2019-04-14T09:16:58Z"@en, "2018-10-15T15:41"@en ; dcterms:description """By a result of Simon it is known that a theory of a coloured linear order has quantifier elimination after naming all unary $L$-definable sets and all $L$-definable binary monotone relations. Motivated by this result we define the notion of monotone theories, theories of linear orders in which binary definable sets have previous description. More precisely, an $\\aleph_0$-saturated structure $M$ is said to be monotone if there exists an $L$-definable linear order $<$ such that every $A$-definable subset of $M^2$ is a finite Boolean combination of unary $A$-definable sets and $A$-definable $<$-monotone relations, in which case we also say that $M$ is monotone with respect to $<$. A theory is said to be monotone if it has a monotone $\\aleph_0$-saturated model. We prove that the class of monotone theories coincides with the class of weakly quasi-o-minimal theories introduced by Kudaibergenov. Moreover, we describe definable linear orders in monotone theories and show that monotonicity of a theory does not depend on the choice of the linear order. Joint work with Predrag Tanovi\\'c."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/69677?expand=metadata"@en ; dcterms:extent "26.0"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: University of Wroclaw"@en ; edm:isShownAt "10.14288/1.0378204"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Postdoctoral"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))"@en ; dcterms:subject "Mathematics"@en, "Mathematical logic and foundations"@en, "Combinatorics"@en ; dcterms:title "Monotone theories"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/69677"@en .