{"paper":{"title":"Namba forcing, weak approximation, and guessing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"John Krueger, Sean Cox","submitted_at":"2016-10-02T17:29:52Z","abstract_excerpt":"We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\\textsf{IGMP}$, $\\textsf{GMP}$ together with $2^\\omega \\le \\omega_2$ is consistent with the existence of an $\\omega_1$-distributive nowhere c.c.c. forcing poset of size $\\omega_1$. We introduce the idea of a weakly guessing model, and prove that many of the strong consequences of the principle $\\textsf{GMP}$ follow from the existence of stationarily many weakly guessing models. Using Namba forcing, we construct a model in which there are stationarily many indestructibly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00319","kind":"arxiv","version":3},"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"}