{"paper":{"title":"Forcing and Construction Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damjan Kalajdzievski, Fulgencio Lopez","submitted_at":"2017-11-29T23:24:32Z","abstract_excerpt":"We investigate forcing and independence questions relating to construction schemes. We show that adding $\\kappa\\geq\\omega_1$ Cohen reals adds a capturing construction scheme. We study the weaker structure of $n$-capturing construction schemes and show that it is consistent to have $n$-capturing construction schemes but no $(n+1)$-capturing construction schemes. We also study the relation of $n$-capturing with the $m$-Knaster hierarchy and show that MA$_{\\omega_1}($K$_m)$ and $n$-capturing are independent if $n\\leq m$ and incompatible if $n>m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11148","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"}