Open Access
2015 Vapnik–Chervonenkis Density on Indiscernible Sequences, Stability, and the Maximum Property
Hunter Johnson
Notre Dame J. Formal Logic 56(4): 583-593 (2015). DOI: 10.1215/00294527-3153597


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 VCind-density and use it to compute the exact VCind-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 Johnson. "Vapnik–Chervonenkis Density on Indiscernible Sequences, Stability, and the Maximum Property." Notre Dame J. Formal Logic 56 (4) 583 - 593, 2015.


Received: 4 January 2013; Accepted: 8 August 2013; Published: 2015
First available in Project Euclid: 30 September 2015

zbMATH: 1372.03064
MathSciNet: MR3403093
Digital Object Identifier: 10.1215/00294527-3153597

Primary: 03C45
Secondary: 68R05

Keywords: NIP , stability , VC-density , VC-dimension

Rights: Copyright © 2015 University of Notre Dame

Vol.56 • No. 4 • 2015
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