Vapnik-Chervonenkis density on indiscernible sequences, stability, and the maximum property
arXiv:1302.5446 · doi:10.1215/00294527-3153597
Abstract
This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on VC_ind-density, and use it to compute the exact VC_ind- density of polynomial inequalities, and a variety of geometric set families. The main technical tool used is the notion of a maximum set system, which we juxtapose to indiscernibles. In the second part of the paper we give a maximum set system analogue to Shelah's characterization of stability using indiscernible sequences.
12 pages