Abstract
We recall that σ-complete MV-algebras are MV-algebras which are σ-complete lattices. Such MV-algebras are always semisimple algebras, and they are exactly those for which there exists an MV-isomorphism with a Bold algebra, i.e., with an algebra of fuzzy sets on a crisp set Ω which contains lΩ, and which is closed under the fuzzy complementation and formation of min{f + g, l}. Belluce [Bel] showed that every semisimple MV-algebra M can be always represented as a Bold algebra of continuous fuzzy sets on the compact Hausdorff space of all maximal ideals of M. And this is an analogue of Stone’s representation theorem for Boolean algebras. Situation with σ-complete MV-algebras is more complicated as we will see below.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
