We prove functorial representation theorems for MV algebras, and for varieties ⌬ obtained from MV algebras by the adding of additional operators corresponding ⌬ w x to natural operations in the real interval 0, 1 , namely PMV algebras, obtained by ⌬ the adding of product, and Ł ⌸ algebras, obtained
A Representation Theorem for MV-algebras
✍ Scribed by Gejza Jenča
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 168 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1432-7643
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📜 SIMILAR VOLUMES
## Abstract Let __M__ be an MV‐algebra and Ω~__M__~ be the set of all __σ__ ‐valuations from __M__ into the MV‐unit interval. This paper focuses on the characterization of MV‐algebras using __σ__ ‐valuations of MV‐algebras and proves that a __σ__ ‐complete MV‐algebra is __σ__ ‐regular, which means
In [9] Mundici introduced a categorical equivalence I' between the category of MV-algebras and the category of abelian .!-groups with strong unit. Using Mundici's functor r, in [a] the authors established an equivalence between the category of perfect MValgebras and the category of abelian f-groups.
## Abstract We prove that the __m__ ‐generated free MV‐algebra is isomorphic to a quotient of the disjoint union of all the __m__ ‐generated free MV^(__n__)^‐algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV^(__n__)^‐algebras and special maps between th
The notion of the ®-compatible sequence of observables on MV algebras is given in this paper, and a version of the Jegorov theorem for this sequence of observables is presented.