@TechReport{DiNola-TR-2004-14, IS = { zkontrolovano 04 Mar 2005 }, UPDATE = { 2005-01-19 }, author = {Di Nola, Antonio and Navara, Mirko }, title = {Set representations of sigma-complete {MV}-algebras}, institution = {Center for Machine Perception, K13133 FEE Czech Technical University}, address = {Prague, Czech Republic}, year = {2004}, month = {December}, type = {Research Report}, number = {{CTU--CMP--2004--14}}, issn = {1213-2365}, pages = {23}, figures = {0}, authorship = {50-50}, psurl = {[DiNola-TR-2004-14.pdf]}, project = {GACR 201/02/1540}, annote = {We characterize {\L}ukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the {\L}ukasiewicz 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 {\L}ukasiewicz tribes.}, keywords = {MV-algebra, sigma-complete MV-algebra, McNaughton function, tribe}, }