Submission date: 21 February 2013.

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.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1302.5446: pdf, ps.