Geodesic
Ample hierarchy
Andreas Baudisch1 ; Amador Martin-Pizarro2 ; Martin Ziegler3
1 Institut für Mathematik Humboldt-Universität zu Berlin D-10099 Berlin, Germany
2 Université de Lyon CNRS Université Lyon 1 Institut Camille Jordan UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
3 Mathematisches Institut Albert-Ludwigs-Universität Freiburg D-79104 Freiburg, Germany
Fundamenta Mathematicae, Tome 224 (2014) no. 2, pp. 97-153.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm224-2-1
Keywords: ample hierarchy geometries stables theories strict generalise construction pseudospace higher dimensions n dimensional pseudospace omega stable n ample yet ample particular pseudospace ample thorough study forking conducted explicit description canonical bases given

Andreas Baudisch 1 ; Amador Martin-Pizarro 2 ; Martin Ziegler 3

1 Institut für Mathematik Humboldt-Universität zu Berlin D-10099 Berlin, Germany
2 Université de Lyon CNRS Université Lyon 1 Institut Camille Jordan UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
3 Mathematisches Institut Albert-Ludwigs-Universität Freiburg D-79104 Freiburg, Germany 
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Andreas Baudisch; Amador Martin-Pizarro; Martin Ziegler. Ample hierarchy. Fundamenta Mathematicae, Tome 224 (2014) no. 2, pp. 97-153. doi : 10.4064/fm224-2-1. http://geodesic.mathdoc.fr/articles/10.4064/fm224-2-1/

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