{"paper":{"title":"High dimensional Ellentuck spaces and initial chains in the Tukey structure of non-p-points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Natasha Dobrinen","submitted_at":"2014-06-05T08:20:41Z","abstract_excerpt":"The generic ultrafilter $\\mathcal{G}_2$ forced by $\\mathcal{P}(\\omega\\times\\omega)/($Fin$\\otimes$Fin) was recently proved to be neither maximum nor minimum in the Tukey order of ultrafilters (in a recent paper of Blass, Dobrinen, and Raghavan), but it was left open where exactly in the Tukey order it lies. We prove that $\\mathcal{G}_2$ is in fact Tukey minimal over its projected Ramsey ultrafilter. Furthermore, we prove that for each $k\\ge 2$, the collection of all nonprincipal ultrafilters Tukey reducible to the generic ultrafilter $\\mathcal{G}_k$ forced by $\\mathcal{P}(\\omega^k)/$Fin$^{\\otim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1291","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"}