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

Abstract

We show that for a number of theories $T^{\ast }$ of model-theoretic interest there is a simpler theory $T$ and $\kappa \ge {\aleph }_0$ such that $T^{\ast }$ is trace equivalent to the theory of $\kappa$-dimensional space over a model of $T$.

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