Dr. Adam Prenosil, from the Institute of Computer Science, Czech Academy of Sciences, will be visiting us (4-13 February 2023) and will give the seminar “Priestley duality for positive MV-algebras” on Wednesday the 8th of February at 11:00 in Sala Riunioni (DipMat).
Abstract: I will present ongoing joint work with Marco Abbadini, which aims to provide a Priestley-type duality for (a subclass of) positive MV-algebras, i.e. negation-free subreducts of MV-algebras. This work draws on two sources. One is the Stone-type duality for locally finite MV-algebras due to Cignoli, Dubuc & Mundici (later extended to weakly locally finite MV-algebras by Cignoli & Marra). The other source is a universal algebraic version of Stone duality due to Keimel & Werner, which covers varieties generated by a finite algebra with a discriminator term. We show how to state the duality for (weakly) locally finite MV-algebras in purely universal algebraic terms and how to extend it to the case of positive MV-algebras. As an application, we show that the free MV-extension of a locally finite positive MV-algebra (the MV-analogue of the free Boolean extension) receives a simple interpretation in dual terms.