Ample hierarchy
Volume 224 / 2014
Fundamenta Mathematicae 224 (2014), 97-153
MSC: Primary 03C45.
DOI: 10.4064/fm224-2-1
Abstract
The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the $n$-dimensional free pseudospace is $\omega $-stable $n$-ample yet not $(n+1)$-ample. In particular, the free pseudospace is not $3$-ample. A thorough study of forking is conducted and an explicit description of canonical bases is given.
