{"paper":{"title":"Martin's Maximum and tower forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Matteo Viale, Sean Cox","submitted_at":"2011-10-07T16:52:41Z","abstract_excerpt":"There are several examples in the literature showing that compactness-like properties of a cardinal $\\kappa$ cause poor behavior of some generic ultrapowers which have critical point $\\kappa$ (Burke \\cite{MR1472122} when $\\kappa$ is a supercompact cardinal; Foreman-Magidor \\cite{MR1359154} when $\\kappa = \\omega_2$ in the presence of strong forcing axioms). We prove more instances of this phenomenon. First, the Reflection Principle (RP) implies that if $\\vec{\\mathcal{I}}$ is a tower of ideals which concentrates on the class $GIC_{\\omega_1}$ of $\\omega_1$-guessing, internally club sets, then $\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1584","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"}