Turkish Journal of Mathematics
Abstract
We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first-order theory of non-Abelian free groups, T_{fg}, is n-ample for any n \in \omega. This result adds to the work of Pillay, which proved that T_{fg} is non-CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in F_{\omega}. Our result provides an alternative proof to the main result of a recent preprint by Ould Houcine and Tent.
DOI
10.3906/mat-1308-6
Keywords
Free groups, pseudo-Anosov homeomorphisms, geometric stability theory
First Page
63
Last Page
80
Recommended Citation
SKLINOS, RIZOS
(2015)
"On ampleness and pseudo-Anosov homeomorphisms in the free group,"
Turkish Journal of Mathematics: Vol. 39:
No.
1, Article 7.
https://doi.org/10.3906/mat-1308-6
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss1/7
