Local dp-rank and VC-density over indiscernible sequences

Authors

Vincent Guingona, Cameron Donnay Hill

Type: Article

Publication Date: 2011-08-12

Citations: 6

View

Abstract

Locations

arXiv (Cornell University)
View

On VC-density over indiscernible sequences

2011-01-01

Vincent Guingona , Cameron Donnay Hill

In this paper, we study VC-density over indiscernible sequences (denoted VC_ind-density). We answer an open question in [1], showing that VC_ind-density is always integer valued. We also show that VC_ind-density … In this paper, we study VC-density over indiscernible sequences (denoted VC_ind-density). We answer an open question in [1], showing that VC_ind-density is always integer valued. We also show that VC_ind-density and dp-rank coincide in the natural way.

View PDF Chat

On VC-density over indiscernible sequences

2011-08-12

Vincent Guingona , Cameron Donnay Hill

On Vapnik‐Chervonenkis density over indiscernible sequences

2014-01-29

Vincent Guingona , Cameron Donnay Hill

In this paper, we study Vapnik‐Chervonenkis density (VC‐density) over indiscernible sequences (denoted VC ind ‐density). We answer an open question in [1], showing that VC ind ‐density is always integer … In this paper, we study Vapnik‐Chervonenkis density (VC‐density) over indiscernible sequences (denoted VC ind ‐density). We answer an open question in [1], showing that VC ind ‐density is always integer valued. We also show that VC ind ‐density and dp‐rank coincide in the natural way.

A linear upper bound in extremal theory of sequences

1994-11-01

Martin Klazar

On the rank function for infinite sets

1976-12-01

Gerhard Hesse , K. Steffens

A Number Theoretic Characterization of Dimension Sequences

1975-01-01

Tom Parker

Density of Integer Sequences

1968-12-01

R. Kaufman

A general upper bound in extremal theory of sequences

1992-01-01

Martin Klazar

Extremal discrepancy behavior of lacunary sequences

2014-10-18

Christoph Aistleitner , Katusi Fukuyama

View PDF Chat

Dedekind Domains and the P-rank of Ext

2017-04-21

Daniel F. V. James

Sperner families of bounded VC-dimension

1997-10-01

R.P. Anstee , Attila Sali

CNED sets: countably negligible for extremal distances

2024-06-25

Dimitrios Ntalampekos

Dominating sequences and tight spaces

1982-02-28

A. I. Veksler

Characterization of weak limits of randomly indexed sequences

2000-11-01

Andrzej Krajka

Unbounded Sequences of Euler-Dedekind Means

1985-10-01

Charles R. Wall

p-Adic Properties of Sequences ofAverages

2001-10-01

一幸畑田

Projective dimensions and almost split sequences

2003-11-21

Dag Madsen

The Borel complexity of ideal limit points

2022-02-28

Xi He , Hang Zhang , Shuguo Zhang

Almost p-ary sequences

2020-02-17

Büşra Özden , Oğuz Yayla

Almost Summable Sequences

1966-12-01

J. P. King

View PDF Chat

Vapnik-Chervonenkis density in some theories without the independence property, I

2015-12-22

Matthias Aschenbrenner , Alf Dolich , Deirdre Haskell +2 more

We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, … We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-minimal theories.

View PDF Chat

Additivity of the dp-rank

2013-07-01

Itay Kaplan , Alf Onshuus , Alexander Usvyatsov

The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank cannot be reduced to the study of its … The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types, and we discuss the possible relations between dp-rank and VC-density.

Vapnik–Chervonenkis Density on Indiscernible Sequences, Stability, and the Maximum Property

2015-01-01

Hunter Johnson

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 … 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.

View PDF Chat

dp-Rank and Forbidden Configurations

2012-12-14

Hunter Johnson

class in n parameters. class in n parameters.

View PDF Chat

Additivity of the dp-rank

2011-09-07

Itay Kaplan , Alf Onshuus , Alexander Usvyatsov

The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of … The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types, and discuss the possible relations between dp-rank and VC-density.

Some new maximum VC classes

2014-02-04

Hunter Johnson

View PDF Chat