Extending Stone duality to multisets and locally finite MV-algebras

Abstract

Stone duality between boolean algebras and inverse limits of ÿnite sets is extended to a duality between locally ÿnite MV-algebras and a category of multisets naturally arising as inverse limits of ÿnite multisets.

MV-closures of Wajsberg hoops and applications

“…Following the work in [7], it may be easily shown that the same dual equivalence between the categories C and MV lf defines a dual equivalence between the categories C * and MV * lf . Hence, it only remains to show that MV * lf is equivalent to WH lf , the category of locally finite Wajsberg hoops.…”

“…In [7] the authors give a dual equivalence between the category of locally finite MValgebras and a certain category of multisets. We will see that the construction given in the previous section allows us to derive a topological duality for locally finite Wajsberg hoops by making minor changes to the corresponding duality for MV-algebras.…”

“…We start by reviewing the duality given in [7]. A supernatural number is a function ν : P → {0, 1, 2, .…”

“…In [7], the authors find a dual equivalence between the category C and the category MV lf of locally finite MV-algebras. By virtue of the construction of the MV-closure of a Wajsberg hoop given in the previous section, we may now modify the previous duality to obtain a corresponding duality for the category of locally finite Wajsberg hoops.…”

A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System

“…For instance, see [28] for a Priestley style duality for MV and [6] for a duality for the class of locally finite MV-algebras.…”