{"paper":{"title":"Ramsey theorem for trees with successor operation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.LO"],"primary_cat":"math.CO","authors_text":"Andy Zucker, David Chodounsk\\'y, Jan Hubi\\v{c}ka, Jaroslav Ne\\v{s}et\\v{r}il, Martin Balko, Mat\\v{e}j Kone\\v{c}n\\'y, Natasha Dobrinen","submitted_at":"2023-11-12T15:13:34Z","abstract_excerpt":"We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees.\n  Our theorem has a number of applications both in finite and infinite combinatorics. For example, we give a short proof of the unrestricted Ne\\v{s}et\\v{r}il-R\\\"odl theorem, and we recover the Graham-Rothschild theorem. Our original motivation came from the study of big Ramsey degrees - various trees used in the study can be viewed as trees with a successor operation. To illustrate this, we gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.06872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}