{"paper":{"title":"A minimal PI cascade with $2^{\\mathfrak{c}}$ minimal ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eli Glasner, Yair Glasner","submitted_at":"2018-01-10T13:55:48Z","abstract_excerpt":"We first improve an old result of McMahon and show that a metric minimal flow whose enveloping semigroup contains less than $2^{\\mathfrak{c}}$ (where ${\\mathfrak{c}} ={2^{\\aleph_0}}$) minimal left ideals is PI. Then we show the existence of various minimal PI flows with many minimal left ideals, as follows. For the acting group $G=SL_2(\\mathbb{R})^\\mathbb{N}$, we construct a metric minimal PI $G$-flow with $\\mathfrak{c}$ minimal left ideals. We then use this example and results established in \\cite{GW-79} to construct a metric minimal PI cascade $(X,T)$ with $\\mathfrak{c}$ minimal left ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03377","kind":"arxiv","version":3},"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"}