{"paper":{"title":"Expansions of real closed fields which introduce no new smooth functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alex Savatovsky, Pantelis E. Eleftheriou","submitted_at":"2018-12-25T18:51:28Z","abstract_excerpt":"We prove the following theorem: let $\\widetilde{\\mathcal R}$ be an expansion of the real field $\\overline{\\mathbb R}$, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a \"semialgebraic chunk\". Then every definable smooth function $f:X\\subseteq \\mathbb R^n\\to \\mathbb R$ with open semialgebraic domain is semialgebraic.\n  Conditions (I) and (II) hold for various d-minimal expansions $\\widetilde{\\mathcal R} = \\langle \\overline{\\mathbb R}, P\\rangle$ of the real field, such as when $P=2^\\mathbb Z$, or $P\\subseteq \\mathbb R$ is an iteration seque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10151","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"}