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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The free roots of the complete graph


Authors: Enrique Casanovas and Frank O. Wagner
Journal: Proc. Amer. Math. Soc. 132 (2004), 1543-1548
MSC (2000): Primary 03C45
Published electronically: October 2, 2003
MathSciNet review: 2053363
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Abstract: 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: e.casanovas@ub.edu

Frank O. Wagner
Affiliation: Institut Girard Desargues, Université Claude Bernard (Lyon 1), 21, avenue Claude Bernard, 69622 Villeurbanne, France
Email: wagner@igd.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07193-4
PII: S 0002-9939(03)07193-4
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.
Article copyright: © Copyright 2003 American Mathematical Society