A model theoretic study of right-angled buildings

TL;DR

This paper explores the model theory of countable right-angled buildings with infinite residues, establishing their stability, axiomatization, and ampleness bounds based on Coxeter graphs, generalizing the free pseudospace.

Contribution

It provides a complete axiomatization and stability analysis of right-angled buildings, linking their properties directly to Coxeter graphs, and extends the understanding of free pseudospace.

Findings

Theories are complete, $ ext{ω}$-stable, and equational.

Bounds on ampleness are derived from Coxeter graphs.

Generalizes and offers an alternative approach to free pseudospace.

Abstract

We study the model theory of countable right-angled buildings with infinite residues. For every Coxeter graph we obtain a complete theory with a natural axiomatisation, which is $\omega$-stable and equational. Furthermore, we provide sharp lower and upper bounds for its degree of ampleness, computed exclusively in terms of the associated Coxeter graph. This generalises and provides an alternative treatment of the free pseudospace.