Weak forms of elimination of imaginaries

Mathematical Logic Quarterly 50 (2):126-140 (2004)

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 and closed subgroups of the Galois group Aut/A). We also characterize when the topology of the Galois group is the quotient topology
Keywords Elimination of imaginaries  canonical base  Galois group  strong type
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DOI 10.1002/malq.200310083
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