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math.LO2011★ 1 cited
Chain conditions in dependent groups
Itay Kaplan, Saharon Shelah
In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly^{2} dependent theories.
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,…