{"paper":{"title":"Definable valuations on ordered fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Franziska Jahnke, Lothar Sebastian Krapp, Philip Dittmann, Salma Kuhlmann","submitted_at":"2022-06-30T14:09:43Z","abstract_excerpt":"We study the definability of convex valuations on ordered fields, with a particular focus on the distinguished subclass of henselian valuations. In the setting of ordered fields, one can consider definability both in the language of rings $\\mathcal{L}_{\\mathrm{r}}$ and in the richer language of ordered rings $\\mathcal{L}_{\\mathrm{or}}$. We analyse and compare definability in both languages and show the following contrary results: while there are convex valuations that are definable in the language $\\mathcal{L}_{\\mathrm{or}}$ but not in the language $\\mathcal{L}_{\\mathrm{r}}$, any $\\mathcal{L}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15301","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/2206.15301/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"}