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Weak forms of elimination of imaginaries
Author(s) -
Casanovas Enrique,
Farré Rafel
Publication year - 2004
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310083
Subject(s) - mathematics , quotient , pure mathematics , group (periodic table) , type (biology) , galois group , algebraically closed field , degree (music) , topology (electrical circuits) , algebra over a field , combinatorics , ecology , organic chemistry , acoustics , biology , chemistry , physics
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)