On the model theory of open generalized polygons

TL;DR

This paper proves that the theory of open generalized n-gons for n≥3 is complete, decidable, and strictly stable, providing new examples in the landscape of stable theories.

Contribution

It establishes the model-theoretic properties of open generalized n-gons, a new class of structures with stable theory.

Findings

The theory is complete for all n≥3.

The theory is decidable.

The theory is strictly stable.

Abstract

We show that for any $n\geq 3$ the theory of open generalized $n$-gons is complete, decidable and strictly stable, yielding a new class of examples in the zoo of stable theories.