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ADDITIVE COVERS AND THE CANONICAL BASE PROPERTY

Part of: Model theory

Published online by Cambridge University Press:  15 June 2022

MICHAEL LOESCH
MICHAEL LOESCH*
Affiliation:
ABTEILUNG FÜR MATHEMATISCHE LOGIK MATHEMATISCHES INSTITUT, ALBERT-LUDWIGS-UNIVERSITÄT FREIBURG ERNST-ZERMELO-STRASSE 1, D-79104, FREIBURG, GERMANY
*
E-mail: [email protected]
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Abstract

We give a new approach to the failure of the Canonical Base Property (CBP) in the so far only known counterexample, produced by Hrushovski, Palacín and Pillay. For this purpose, we will give an alternative presentation of the counterexample as an additive cover of an algebraically closed field. We isolate two fundamental weakenings of the CBP, which already appeared in work of Chatzidakis and Moosa-Pillay and show that they do not hold in the counterexample. In order to do so, a study of imaginaries in additive covers is developed. As a by-product of the presentation, we observe that a pure binding-group-theoretic account of the CBP is unlikely.

Keywords

stabilityinternalityadditive coversCBP

MSC classification

Primary: 03C45: Classification theory, stability and related concepts
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 1 , March 2023 , pp. 118 - 144
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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