Journals / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 1
On ampleness and pseudo-Anosov homeomorphisms in the free group
- Pages
- 63–80
- DOI
- —
Abstract
We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first-order theory of non-Abelian free groups, Tfg, is n-ample for any n \in w. This result adds to the work of Pillay, which proved that Tfg is non-CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in Fw. Our result provides an alternative proof to the main result of a recent preprint by Ould Houcine and Tent.
Özet
We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first-order theory of non-Abelian free groups, Tfg, is n-ample for any n \in w. This result adds to the work of Pillay, which proved that Tfg is non-CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in Fw. Our result provides an alternative proof to the main result of a recent preprint by Ould Houcine and Tent.