{"paper":{"title":"Actions of trees on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Martino Lupini","submitted_at":"2016-11-19T05:53:04Z","abstract_excerpt":"We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary Gowers Ramsey theorem for multiple tetris operations, the infinitary Hales--Jewett theorems (for both located and nonlocated words), and the Farah--Hindman--McLeod Ramsey theorem for layered actions on partial semigroups. We also establish a polynomial version of our main result, recovering the polynomial Milliken--Taylor theorem of Bergelson--Hindman--Williams as a particular case. We present applications of our Rams"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06312","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"}