Vincent Guingona: VC-density, dp-rank, and op-dimension.

Model Theory Seminar
Date: Monday, November 11, 2013
Time: 5:00PM – 6:30PM
Location: Wean 8220
Vincent Guingona (University of Notre Dame)

Title:  VC-density, dp-rank, and op-dimension.

Abstract:  I talk about my recent work joint with Cameron Hill on various notions of rank and dimension in NIP theories.  I begin with a discussion of dp-rank and it’s relation to VC-density.  I show that dp-rank and VC-density over indiscernible sequences coincide in the natural way.  Then, I talk about the notion of op-dimension, which is a new rank related to both dp-rank and Shelah’s 2-rank.  I show that op-dimension bounds dp-rank, is subadditive, and generalizes dimension in o-minimal theories.


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