{"paper":{"title":"Dimension in the realm of transseries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.LO","authors_text":"Joris van der Hoeven, Lou van den Dries, Matthias Aschenbrenner","submitted_at":"2016-07-25T08:02:57Z","abstract_excerpt":"Let $\\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\\mathbb T}^n$, also in relation to its codimension in the ambient space ${\\mathbb T}^n$. The case of dimension $0$ is of special interest, and can be characterized both in topological terms (discreteness) and in terms of the Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results by the authors from \"Asymptotic Differential Algebra and Model Theory of Transseries\", the axiomatic framework for \"dimension\" in [L. van den Dries, \"Dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07173","kind":"arxiv","version":2},"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"}