On ampleness and pseudo-Anosov homeomorphisms in the free group
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.
Anahtar Kelimeler:
Free groups, pseudo-Anosov homeomorphisms, geometric stability theory
On ampleness and pseudo-Anosov homeomorphisms in the free group
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.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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On ampleness and pseudo-Anosov homeomorphisms in the free group
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