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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The free roots of the complete graph
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by Enrique Casanovas and Frank O. Wagner PDF
Proc. Amer. Math. Soc. 132 (2004), 1543-1548 Request permission


There is a model-completion $T_n$ of the theory of a (reflexive) $n$-coloured graph $\langle X,R_1,\ldots ,R_n\rangle$ such that $R_n$ is total, and $R_i\circ R_j\subseteq R_{i+j}$ for all $i,j$. For $n>2$, the theory $T_n$ is not simple, and does not have the strict order property. The theories $T_n$ combine to yield a non-simple theory $T_\infty$ without the strict order property, which does not eliminate hyperimaginaries.
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Additional Information
  • Enrique Casanovas
  • Affiliation: Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Baldiri Reixac s/n, 08028 Barcelona, Spain
  • Email:
  • Frank O. Wagner
  • Affiliation: Institut Girard Desargues, Université Claude Bernard (Lyon 1), 21, avenue Claude Bernard, 69622 Villeurbanne, France
  • Email:
  • Received by editor(s): March 27, 2002
  • Received by editor(s) in revised form: January 8, 2003
  • Published electronically: October 2, 2003
  • Additional Notes: The first author was partially supported by grant PB98-1231 of the Spanish Ministry of Science and Education
    This work was partially done while the first author was visiting the Université Claude Bernard, and while the second author was visiting the Universitat de Barcelona; both authors would like to thank their respective hosts
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1543-1548
  • MSC (2000): Primary 03C45
  • DOI:
  • MathSciNet review: 2053363