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1 results

  • Loomis-sikorski theorem for σ-complete MV-algebras and ℓ-groups

  • Part of
  • Anatolij Dvurečenskij
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 68 / Issue 2 / April 2000
    Published online by Cambridge University Press:
    09 April 2009, pp. 261-277
    Print publication:
    April 2000
    • Article
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  • We show that every σ-complete MV-algebra is an MV-σ-homomorphic image of some σ-complete MV- algebra of fuzzy sets, called a tribe, which is a system of fuzzy sets of a crisp set Ω containing 1Ω and closed under fuzzy complementation and formation of min {∑nfn, 1}. Since a tribe is a direct generalization of a σ-algebra of crisp subsets, the representation theorem is an analogue of the Loomis-Sikorski theorem for MV-algebras. In addition, this result will be extended also for Dedekind σ-complete ℓ-groups with strong unit.