{"paper":{"title":"Hyperclass Forcing in Morse-Kelley Class Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carolin Antos, Sy-David Friedman","submitted_at":"2015-10-14T13:25:22Z","abstract_excerpt":"In this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK$^{**}$. We define this forcing by using a symmetry between MK$^{**}$ models and models of ZFC$^-$ plus there exists a strongly inaccessible cardinal (called SetMK$^{**}$). We develop a coding between $\\beta$-models $\\mathcal{M}$ of MK$^{**}$ and transitive models $M^+$ of SetMK$^{**}$ which will allow us to go from $\\mathcal{M}$ to $M^+$ and vice versa. So instead of forcing with a hyperclass in MK$^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04082","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"}