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Density of compressible types and some consequences

  • Martin Bays

    Universität Münster, Germany; University of Oxford, UK

  • Itay Kaplan

    Hebrew University of Jerusalem, Israel

  • Pierre Simon

    University of California, Berkeley, USA
Density of compressible types and some consequences cover

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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 this article

Martin Bays, Itay Kaplan, Pierre Simon, Density of compressible types and some consequences. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1423