{"paper":{"title":"Canonical reconstruction and forcing absoluteness of standard structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.LO","authors_text":"Tomasz Kania","submitted_at":"2026-06-01T21:12:34Z","abstract_excerpt":"We isolate a simple preservation principle governing when it is absolute, between transitive models of set theory, that a given algebraic or topological-algebraic structure has a standard form $F(X)$ indexed by a set $X$. The principle is: if the index $X$ (or a proxy for it) can be recovered from $F(X)$ by a uniform definable construction, then the class of structures isomorphic to some~$F(X)$ is downward absolute from forcing extensions. Answering a question raised by Noah Schweber, we deduce in particular that no group that fails to be a full symmetric group in the ground model can become o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02898","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/2606.02898/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"}