{"paper":{"title":"Indestructibility properties of remarkable cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Victoria Gitman, Yong Cheng","submitted_at":"2014-11-10T19:27:07Z","abstract_excerpt":"Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of $L(\\mathbb R)$ is absolute for proper forcing. Here, we study the indestructibility properties of remarkable cardinals. We show that if $\\kappa$ is remarkable, then there is a forcing extension in which the remarkability of $\\kappa$ becomes indestructible by all $\\lt\\kappa$-closed $\\leq\\kappa$-distributive forcing and all two-step iterations of the form ${\\rm Add}(\\kappa,\\theta)*\\dot{\\mathbb R}$, where $\\dot{\\mathbb R}$ is forced to b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2551","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"}