{"paper":{"title":"Bounded forcing axioms and Baumgartner's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Aspero, Marcin Sabok, Miguel Angel Mota, Sy-David Friedman","submitted_at":"2011-02-11T03:50:13Z","abstract_excerpt":"We study the spectrum of forcing notions between the iterations of $\\sigma$-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of $\\alpha$-proper forcings for indecomposable countable ordinals as well as the Axiom A forcings. We focus on the bounded forcing axioms for the hierarchy of $\\alpha$-proper forcings and connect them to a hierarchy of weak club guessing principles. We show that they are, in a sense, dual to each other. In particular, these weak club guessing principles separate the bounded forcing axioms for distinct countable indecomposable ordinals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2275","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"}