Median algebra with a retraction: an example of variety closed under   natural extension

Reference : Median algebra with a retraction: an example of variety closed under natural extension


	Document type :	Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/23652

Title :	Median algebra with a retraction: an example of variety closed under natural extension
Language :	English
Author, co-author :	Teheux, Bruno [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	14-Jan-2016
Event name :	The Logic Seminar (Università degli Studi di Milano and Università degli Studi dell'Insubria)
Event date :	January 14, 2016
Event organizer :	Università degli Studi di Milano and Università degli Studi dell'Insubria
Event place (city) :	Milan
Event country :	Italy
Keywords :	[en] natural dualities ; natural extension ; median algebras
Abstract :	[en] The notion of natural extension can be defined for any algebra in an IRF-prevariety. In this talk, we introduce a way to extend functions between algebras to multifunctions between their natural extensions, and we give sufficient conditions under which we can assume that these multifunctions are functions. We illustrate these constructions for the variety of median algebras, and we prove that retractions over median algebras are preserved by natural extensions.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/23652

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