MV algebras and Multisets
by
Daniele Mundici
University of Florence
Coauthors: E.Dubuc, R.Cignoli

We establish a duality between a category C of multisets and locally finite MV algebras. Multisets in C are closed under the basic set-theoretic operations. Every multiset is the inverse limit of finite multisets. To take care of infinite multisets and infinite multiplicities one needs ``supernatural numbers'', a well known generalization of natural numbers that Serre, Glimm, Fuchs, Shatz and others used for classification purposes. The complete Heyting algebra S of supernatural numbers has a natural topology. An object in C is just a continuous map f:X --> S, where X is a boolean space. If one restricts to constant assignments of multiplicity one then our duality coincides with Stone duality.

Date received: May 14, 2003