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math.LO2011★ 5 cited
Additivity of the dp-rank
Itay Kaplan, Alf Onshuus, Alexander Usvyatsov
The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types,…
math.LO2011★ 7 cited
The algebraic numbers definable in various exponential fields
Jonathan Kirby, Angus Macintyre, Alf Onshuus
We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular or the Zilber fields, all real abelian algebraic numbers are pointwise def…