{"paper":{"title":"Incompatible category forcing axioms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Aspero, Matteo Viale","submitted_at":"2018-05-22T16:42:13Z","abstract_excerpt":"Given a cardinal $\\lambda$, category forcing axioms for $\\lambda$-suitable classes $\\Gamma$ are strong forcing axioms which completely decide the theory of the Chang model $\\mathcal C_\\lambda$, modulo generic extensions via forcing notions from $\\Gamma$. $\\mathsf{MM}^{+++}$ was the first category forcing axiom to be isolated (by the second author). In this paper we present, without proofs, a general theory of category forcings, and prove the existence of $\\aleph_1$-many pairwise incompatible category forcing axioms for $\\omega_1$-suitable classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08732","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"}