Geodesic
Ample hierarchy
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
Fundamenta Mathematicae, Tome 224 (2014) no. 2, pp. 97-153 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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