Density of compressible types and some consequences
Logic
2026-04-02 v3
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.
Cite
@article{arxiv.2107.05197,
title = {Density of compressible types and some consequences},
author = {Martin Bays and Itay Kaplan and Pierre Simon},
journal= {arXiv preprint arXiv:2107.05197},
year = {2026}
}
Comments
v2: New corollary 6.34 on stable reducts; minor fixes elsewhere; numbering changed in section 6. v3: Minor revisions; numbering changed in section 6; accepted for publication in JEMS