(Joint work with Hugo R.O. Ribeiro (IME-USP))
In this third talk, we focus on constructions of multirings associated with real semigroups:
(i) we describe further properties of the functor Q, the reflection (= left adjoint functor) of the natural inclusion of the category of real reduced multirings into the category of pre-ordered multirings and explore some of these properties;
(ii) by the employ of sheaf-theoretic methods, we characterize the real reduced hyperrings as certain "geometric" von Neumann regular real hyperring and describe the functor V, "geometric" von Neumann regular hull of a multiring;
(iii) we present some interesting logical-algebraic interactions between the functors Q and V that are useful to describe the Witt ring of a real semigroup (or real reduced multiring). | 
