Building-like geometries of finite Morley Rank

TL;DR

This paper constructs specific geometries of finite Morley rank that are almost strongly minimal, 2-ample but not 3-ample, for any n ≥ 6, advancing understanding in model theory and geometric structures.

Contribution

It introduces new geometries of finite Morley rank with particular ampleness properties, expanding the class of known structures in model theory.

Findings

Constructs geometries of type with n ≥ 6

Shows these geometries are 2-ample but not 3-ample

Advances understanding of ampleness in finite Morley rank geometries

Abstract

For any $n\geq 6$ we construct almost strongly minimal geometries of type $\bullet \overset{n}{-} \bullet \overset{n}{-}\bullet$ which are $2$-ample but not $3$-ample.