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Original Paper
Weak forms of elimination of imaginaries
Article first published online: 3 FEB 2004
DOI: 10.1002/malq.200310083
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
Casanovas, E. and Farré, R. (2004), Weak forms of elimination of imaginaries. Mathematical Logic Quarterly, 50: 126–140. doi: 10.1002/malq.200310083
Publication History
- Issue published online: 3 FEB 2004
- Article first published online: 3 FEB 2004
- Manuscript Accepted: 13 NOV 2003
- Manuscript Revised: 6 NOV 2003
- Manuscript Received: 9 APR 2003
- Abstract
- References
- Cited By
Keywords:
- Elimination of imaginaries;
- canonical base;
- strong type;
- Galois group
Abstract
We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A ⊆ B ⊆ acl(A) and closed subgroups of the Galois group Aut(acl(A)/A). We also characterize when the topology of the Galois group is the quotient topology. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)