Displaying similar documents to “On dual Ramsey theorems for relational structures”

Relational quotients

Miodrag Sokić (2013)

Fundamenta Mathematicae

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Let 𝒦 be a class of finite relational structures. We define ℰ𝒦 to be the class of finite relational structures A such that A/E ∈ 𝒦, where E is an equivalence relation defined on the structure A. Adding arbitrary linear orderings to structures from ℰ𝒦, we get the class 𝒪ℰ𝒦. If we add linear orderings to structures from ℰ𝒦 such that each E-equivalence class is an interval then we get the class 𝒞ℰ[𝒦*]. We provide a list of Fraïssé classes among ℰ𝒦, 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*]. In addition,...

Gaps and dualities in Heyting categories

Jaroslav Nešetřil, Aleš Pultr, Claude Tardif (2007)

Commentationes Mathematicae Universitatis Carolinae

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We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones. ...

Completion of partially ordered sets

Sergey A. Solovyov (2006)

Discussiones Mathematicae - General Algebra and Applications

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The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.