{"paper":{"title":"Guessing models and the approachability ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Boban Velickovic, Rahman Mohammadpour","submitted_at":"2018-02-27T19:24:08Z","abstract_excerpt":"Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call ${\\rm GM}^+(\\omega_3,\\omega_1)$ holds. This principle implies ${\\rm ISP}(\\omega_2)$ and ${\\rm ISP}(\\omega_3)$, and hence the tree property at $\\omega_2$ and $\\omega_3$, the Singular Cardinal Hypothesis, and the failure of the weak square principle $\\square(\\omega_2,\\lambda)$, for all regular $\\lambda \\geq \\omega_2$. In addition, it implies that the restriction of the approachability ideal $I[\\omega_2]$ to the set of ordinals of cofinality $\\omega_1$ is the non stationary id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10125","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"}