Density of compressible types and some consequences

TL;DR

This paper investigates the density of compressible types within NIP theories, extending machine learning results to obtain uniform honest definitions and construct models.

Contribution

It extends a machine learning bound to prove density of compressible types, enabling explicit honest definitions and model construction in NIP theories.

Findings

Proves density of compressible types in NIP theories.

Provides explicit uniform honest definitions for NIP formulas.

Constructs compressible models in countable NIP theories.

Abstract

We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we obtain explicit uniform honest definitions for NIP formulas (answering a question of Eshel and the second author), and build compressible models in countable NIP theories.