{"paper":{"title":"Forcing and the Halpern-L\\\"auchli Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dan Hathaway, Natasha Dobrinen","submitted_at":"2017-06-25T21:27:01Z","abstract_excerpt":"We investigate the effects of various forcings on several forms of the Halpern-L\\\"auchli Theorem. For inaccessible $\\kappa$, we show they are preserved by forcings of size less than $\\kappa$. Combining this with work of Zhang in \\cite{Zhang17} yields that the polarized partition relations associated with finite products of the $\\kappa$-rationals are preserved by all forcings of size less than $\\kappa$ over models satisfying the Halpern-L\\\"auchli Theorem at $\\kappa$. We also show that the Halpern-L\\\"auchli Theorem is preserved by ${{<}\\kappa}$-closed forcings assuming $\\kappa$ is measurable, fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08174","kind":"arxiv","version":4},"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"}