On forking and definability of types in some dp-minimal theories

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.Comment: Appeared previously as an appendix in arXiv:1210.447

Left-ordered inp-minimal groups

We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2

Witnessing dp-rank

We prove that in NTP_2 theories if p is a dependent type with dp-rank >= \kappa, then this can be witnessed by indiscernible sequences of tuples satisfying p. If p has dp-rank infinity, then this can be witnessed by singletons (in any theory)

On uniform definability of types over finite sets

In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.Comment: 17 pages, 0 figure