{"paper":{"title":"On ampleness and pseudo-Anosov homeomorphisms in the free group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Rizos Sklinos","submitted_at":"2014-09-30T15:35:17Z","abstract_excerpt":"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, that proved that $T_{fg}$ is non CM -trivial. The sequence witnessing ampleness is a sequence of primitive elements in $F_{\\omega}$.\n  Our result provides an alternative proof to the main result of a preprint by Ould Houcine-Tent.\n  We also add an appendix in which we make a few remarks on Sela's paper on imaginaries in torsion free hyperbolic groups. In particular we give alternative trans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8599","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}