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The definable multiplicity property and generic automorphisms

✍ Scribed by Hirotaka Kikyo; Anand Pillay

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
106 KB
Volume
106
Category
Article
ISSN
0168-0072

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✦ Synopsis

Let T be a strongly minimal theory with quantiΓΏer elimination. We show that the class of existentially closed models of T βˆͺ {" is an automorphism"} is an elementary class if and only if T has the deΓΏnable multiplicity property, as long as T is a ΓΏnite cover of a strongly minimal theory which does have the deΓΏnable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T βˆͺ {" i is an automorphism": i = 1; 2} is an elementary class if and only if T has the deΓΏnable multiplicity property.

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