Model Theory of Scattered Piecewise Interpretable Hilbert Spaces

TL;DR

This paper explores the model theory of scattered piecewise interpretable Hilbert spaces, linking their structure to key model theoretic concepts like canonical bases and ranks, thus advancing understanding of their foundational properties.

Contribution

It establishes new connections between Hilbert space structure theorems and core model theoretic notions, providing a novel theoretical framework.

Findings

Link between Hilbert space structure and model theoretic concepts

Characterization of scattered piecewise interpretable Hilbert spaces

Insights into canonical bases and model ranks in this context

Abstract

We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of canonical bases, one-basedness and model theoretic ranks.