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

TL;DR

The paper demonstrates that certain complex theories can be simplified to theories of infinite-dimensional spaces over models of a base theory, establishing trace equivalence.

Contribution

It introduces a method to represent complex theories as theories of infinite-dimensional spaces over simpler base theories, simplifying their analysis.

Findings

Certain theories are trace equivalent to theories of infinite-dimensional spaces.

This equivalence simplifies the understanding of complex model-theoretic theories.

Abstract

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