Algebraic Characterization of FO for Scattered Linear Orderings

Authors Alexis Bès, Olivier Carton

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Alexis Bès
Olivier Carton

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Alexis Bès and Olivier Carton. Algebraic Characterization of FO for Scattered Linear Orderings. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 67-81, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked product, and recognizability by finite aperiodic semigroups which satisfy some additional equation.
  • linear orderings
  • first-order logic
  • semigroups
  • rational sets


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