{"paper":{"title":"Adding a non-reflecting weakly compact set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody","submitted_at":"2017-01-16T17:20:43Z","abstract_excerpt":"For $n<\\omega$, we say that the $\\Pi^1_n$-reflection principle holds at $\\kappa$ and write $\\text{Refl}_n(\\kappa)$ if and only if $\\kappa$ is a $\\Pi^1_n$-indescribable cardinal and every $\\Pi^1_n$-indescribable subset of $\\kappa$ has a $\\Pi^1_n$-indescribable proper initial segment. The $\\Pi^1_n$-reflection principle $\\text{Refl}_n(\\kappa)$ generalizes a certain stationary reflection principle and implies that $\\kappa$ is $\\Pi^1_n$-indescribable of order $\\omega$. We define a forcing which shows that the converse of this implication can be false in the case $n=1$. Moreover, we prove that if $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04358","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1701.04358/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}