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

English

Teheux, Bruno[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

14-Jan-2016

The Logic Seminar (Università degli Studi di Milano and Università degli Studi dell'Insubria)

January 14, 2016

Università degli Studi di Milano and Università degli Studi dell'Insubria

Milan

Italy

[en] natural dualities ; natural extension ; median algebras

[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.