{"paper":{"title":"Easton's theorem for the tree property below aleph_omega","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sarka Stejskalova","submitted_at":"2019-07-08T17:41:30Z","abstract_excerpt":"Starting with infinitely many supercompact cardinals, we show that the tree property at every cardinal $\\aleph_n$, $1 < n <\\omega$, is consistent with an arbitrary continuum function below $\\aleph_\\omega$ which satisfies $2^{\\aleph_n} > \\aleph_{n+1}$, $n<\\omega$. Thus the tree property has no provable effect on the continuum function below $\\aleph_\\omega$ except for the restriction that the tree property at $\\kappa^{++}$ implies $2^\\kappa>\\kappa^+$ for every infinite $\\kappa$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03737","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"}