Weak forms of elimination of imaginaries | Zendy

Casanovas Enrique | Zendy; Farré Rafel | Zendy

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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)

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