{"paper":{"title":"Reduced powers of Souslin trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ari Meir Brodsky, Assaf Rinot","submitted_at":"2015-07-20T20:53:28Z","abstract_excerpt":"We study the relationship between a $\\kappa$-Souslin tree $T$ and its reduced powers $T^\\theta/\\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\\theta$, whereas here, tools are developed for controlling different powers simultaneously. As a sample corollary, we obtain the consistency of an $\\aleph_6$-Souslin tree $T$ and a sequence of uniform ultrafilters $\\langle \\mathcal U_n\\mid n<6\\rangle$ such that $ T^{\\aleph_n}/\\mathcal U_n$ is $\\aleph_6$-Aronszajn iff $n<6$ is not a prime number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05651","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"}