{"paper":{"title":"A model of the generic Vop\\v{e}nka principle in which the ordinals are not Mahlo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Joel David Hamkins, Victoria Gitman","submitted_at":"2017-06-02T20:34:23Z","abstract_excerpt":"The generic Vop\\v{e}nka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vop\\v{e}nka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vop\\v{e}nka scheme is relatively consistent with the existence of a $\\Delta_2$-definable class containing no regular cardinals. In such a model, there can be no $\\Sigma_2$-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00843","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"}