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arXiv · 1302.5446

Vapnik-Chervonenkis density on indiscernible sequences, stability, and the maximum property

Hunter R. Johnson
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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.

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Hunter R. Johnson. 2013-08-08. Vapnik-Chervonenkis density on indiscernible sequences, stability, and the maximum property. https://doi.org/10.1215/00294527-3153597

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