Model-theoretic independence in the Banach lattices $L_p(\mu)$

TL;DR

This paper explores model-theoretic stability and independence in Banach lattices of the form L_p, providing characterizations and demonstrating the existence of canonical bases within these structures.

Contribution

It introduces a novel analysis-based characterization of non-dividing and proves the existence of canonical bases in L_p Banach lattices.

Findings

Non-dividing characterized via analysis concepts

Canonical bases exist as tuples of real elements

Advances understanding of model-theoretic properties in Banach lattices

Abstract

We study model-theoretic stability and independence in Banach lattices of the form $L_p(X,U,\mu)$, where $1 \leq p < \infty$. We characterize non-dividing using concepts from analysis and show that canonical bases exist as tuples of real elements.