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March 2008 Canonical bases in excellent classes
Tapani Hyttinen, Olivier Lessmann
J. Symbolic Logic 73(1): 165-180 (March 2008). DOI: 10.2178/jsl/1208358747

Abstract

We show that any (atomic) excellent class 𝔎 can be expanded with hyperimaginaries to form an (atomic) excellent class 𝔎eq which has canonical bases. When 𝔎 is, in addition, of finite U-rank, then 𝔎eq 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 𝔎 gives rise to an excellent class, which is simple if 𝔎 is of finite U-rank.

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Tapani Hyttinen. Olivier Lessmann. "Canonical bases in excellent classes." J. Symbolic Logic 73 (1) 165 - 180, March 2008. https://doi.org/10.2178/jsl/1208358747

Information

Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1154.03012
MathSciNet: MR2387937
Digital Object Identifier: 10.2178/jsl/1208358747

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 1 • March 2008
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