English

Trace definability III: Infinite dimensional space over a model of $T$

Logic 2026-05-13 v1

Abstract

We show that for a number of theories TT^* of model-theoretic interest there is a simpler theory TT and κ0\kappa \ge \aleph_0 such that TT^* is trace equivalent to the theory of κ\kappa-dimensional space over a model of TT.

Keywords

Cite

@article{arxiv.2605.12337,
  title  = {Trace definability III: Infinite dimensional space over a model of $T$},
  author = {Erik Walsberg},
  journal= {arXiv preprint arXiv:2605.12337},
  year   = {2026}
}

Comments

This is the third in a series of papers consisting of cleaned up and strengthened versions of parts of arXiv:2504.05566v1