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Canonical bases in excellent classes

Published online by Cambridge University Press:  12 March 2014

Tapani Hyttinen  and
Olivier Lessmann
Tapani Hyttinen
Affiliation:
Department of Mathematics and Statistics, P.O. BOX 4, 00014, University of Helsinki, Finland, E-mail: tapani.hyttinen@helsinki.fi
Olivier Lessmann
Affiliation:
Collège Rousseau, Case Postale 216, 1211 Geneva 28, Switzerland, E-mail: lessmann@gmail.com
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Abstract

We show that any (atomic) excellent class can be expanded with hyperimaginaries to form an (atomic) excellent class which has canonical bases. When is, in addition, of finite U-rank, then is also simple and has a full canonical bases theorem. This positive situation contrasts starkly with homogeneous model theory for example, where the eq-expansion may fail to be homogeneous. However, this paper shows that expanding an ω-stable, homogeneous class gives rise to an excellent class, which is simple if is of finite U-rank.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 1 , March 2008 , pp. 165 - 180
Copyright
Copyright © Association for Symbolic Logic 2008

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