Submission date: 26 May 2010. Revised on 7 September 2011.

Abstract:

The main result is the proof of the linearity of the dp-rank.
We also prove that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types and discuss the possible relations between dp-rank and VC-density.

Mathematics Subject Classification:

Keywords and phrases: dependent theories, dp-minimality

Full text: pdf (version of May 2010: pdf, dvi, ps).