The $\sigma$-complete MV-algebras which have enough states
Volume 103 / 2005
Colloquium Mathematicum 103 (2005), 121-130
MSC: Primary 06D35; Secondary
03B52, 03E72, 06C15, 06D30, 06D50, 28E10.
DOI: 10.4064/cm103-1-13
Abstract
We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce $\sigma $-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of $\sigma $-complete MV-algebras which are isomorphic to Łukasiewicz tribes.
