Abstract
An MV-algebra A is said to be σ-complete if its underlying lattice is closed under countable suprema. It follows that A is semisimple, whence it is isomorphic to an MV-algebra A* of continuous [0,1]-valued functions defined on some compact Hausdorff space X.
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References
Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D. (2000). Algebraic foundations of many-valued reasoning, Volume 7 of Trends in Logic. Dordrecht: Kluwer.
Riečan, B., Neubrunn, T. (1997). Integral, Measure, and Ordering. Dordrecht: Kluwer.
Klement, E. P., Mesiar, R., Pap, E. (2000). Triangular norms, Trends in Logic, Vol. 8. Dordrecht: Kluwer.
Stone, M. H. (1949). Boundedness properties in function-lattices. Canadian Journal of Mathematics, 1.2, 176–186.
Nakano, H. (1941). Über das System aller stetigen Funktionen auf einem topologischen Raum. Proceedings of the Imperial Academy. Tokyo, 17, 308–310.
Sikorski, R. (1960). Boolean Algebras. Ergebnisse Math. Grenzgeb. Berlin: Springer.
Mundici, D. (1999). Tensor products and the Loomis–Sikorski theorem for MV-algebras, Advances in Applied Mathematics, 22, 227–248.
Dvurečenskij, A. (2000). Loomis–Sikorski theorem for \(\sigma\)-complete MV-algebras and \(\ell\)-groups, Journal of the Australian Mathematical Society, 68, 261–277.
Butnariu, D., Klement, E. P. (1995). Triangular norm-based measures and games with fuzzy coalitions. Dordrecht: Kluwer.
Cignoli, R., Mundici, D. (2006). Stone duality for Dedekind \(\sigma\)-complete \(\ell\)-groups with order-unit. Journal of Algebra, 302, 848–861.
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Mundici, D. (2011). The MV-Algebraic Loomis–Sikorski Theorem. In: Advanced Łukasiewicz calculus and MV-algebras. Trends in Logic, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0840-2_11
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DOI: https://doi.org/10.1007/978-94-007-0840-2_11
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