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 ω-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-1,
author = {Andreas Baudisch and Amador Martin-Pizarro and Martin Ziegler},
title = {Ample hierarchy},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {97-153},
zbl = {06269372},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-1}
}
Andreas Baudisch; Amador Martin-Pizarro; Martin Ziegler. Ample hierarchy. Fundamenta Mathematicae, Tome 227 (2014) pp. 97-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-1/