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In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory. [ABSTRACT FROM AUTHOR]

An explicit categorical equivalence is defined between a proper subvariety of the class of PMV -algebras, as defined by Di Nola and Dvurečenskij, to be called PMV f -algebras, and the category of semi-low f u -rings. This categorical representation is done using the prime spectrum of the MV -algebras, through the equivalence between MV -algebras and l u -groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low f u -rings associated to Boolean algebras are characterized. [ABSTRACT FROM AUTHOR]

We introduce the variety of Many-Valued-Weak rigs (MVW-rigs). We provide an axiomatisation and establish, in this context, basic properties about ideals, homomorphisms, quotients and radicals. This new class contains the class of product MV-algebras presented by Di Nola and Dvurečenskij in 2001 and by Montagna in 2005. The main result is the compactness of the prime spectrum of this new class, endowed with the co-Zariski topology as defined by Dubuc and Poveda in 2010. [ABSTRACT FROM AUTHOR]

Studying relationships between recursion theory and categorical theory, can find properties of the recursive universe that can be represented by universal properties. It is possible to generalize in some respects this universe to search examples of recursive properties that are not from the arithmetical universe and well understood from other perspectives, the Gödel's incompleteness theorem. [ABSTRACT FROM AUTHOR]