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On the canonical base property

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Abstract

We give an example of a finite rank, in fact \(\aleph _{1}\)-categorical, theory where the canonical base property (CBP) fails. In fact, we give a “group-like” example in a sense that we will describe below. We also prove, in a finite Morley rank context, that if all definable Galois groups are “rigid,” then \(T\) has the CBP.

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Acknowledgments

The research leading to these results has received funding for the first author from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 291111. The second author was partially supported by research project MTM 2011-26840 of the Spanish government and research project 2009SGR 00187 of the Catalan government. The third author was supported by EPSRC Grant EP/I002294/1 and also by the Max Planck Institute in Bonn. Also many thanks to the referee for carefully reading the paper and making helpful suggestions.

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Authors and Affiliations

  1. Hebrew University of Jerusalem, Jerusalem, Israel

    Ehud Hrushovski

  2. Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001 , Barcelona, Spain

    Daniel Palacín

  3. University of Leeds, Leeds, England

    Anand Pillay

Authors
  1. Ehud Hrushovski
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  2. Daniel Palacín
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  3. Anand Pillay
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Correspondence to Anand Pillay.

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Hrushovski, E., Palacín, D. & Pillay, A. On the canonical base property. Sel. Math. New Ser. 19, 865–877 (2013). https://doi.org/10.1007/s00029-013-0129-3

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  • DOI: https://doi.org/10.1007/s00029-013-0129-3

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