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Coordinatizing some concrete MV algebras and a decomposition theorem

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Abstract

MV algebras are the Lindenbaum–Tarski algebras of Łukasiewicz many-valued logics. From work of D. Mundici, countable such algebras correspond to certain AF C*-algebras. M. Lawson and P. Scott gave a coordinatization theorem for them, representing any countable MV-algebra as the lattice of principal ideals of an AF Boolean inverse monoid. In this note, we give two concrete examples of such a coordinatization, one for \({\mathbb {Q}}\cap [0,1]\) and another for the so-called Chang algebra. We also discuss Bratteli diagram techniques to further the coordinatization program.

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Acknowledgements

The authors would like to thank Mark Lawson and the anonymous referee for many insightful comments that have greatly contributed to this work.

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Authors and Affiliations

  1. Department of Mathematics and Statistics and School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    W. Lu

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    P. J. Scott

Authors
  1. W. Lu
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  2. P. J. Scott
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Corresponding author

Correspondence to P. J. Scott.

Additional information

Communicated by Benjamin Steinberg.

W. Lu: Research supported by an NSERC CGS-M scholarship. P. J. Scott: Research supported by an NSERC Discovery grant.

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Lu, W., Scott, P.J. Coordinatizing some concrete MV algebras and a decomposition theorem. Semigroup Forum 98, 213–233 (2019). https://doi.org/10.1007/s00233-018-9920-y

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  • DOI: https://doi.org/10.1007/s00233-018-9920-y

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