{"paper":{"title":"The isomorphism class of the shift map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Will Brian","submitted_at":"2019-04-22T14:49:38Z","abstract_excerpt":"The \\emph{shift map} $\\sigma$ is the self-homeomorphism of $\\omega^* = \\beta\\omega \\setminus \\omega$ induced by the successor function $n \\mapsto n+1$ on $\\omega$. We prove that the isomorphism classes of $\\sigma$ and $\\sigma^{-1}$ cannot be separated by a Borel set in $\\mathcal H(\\omega^*)$, the space of all self-homeomorphisms of $\\omega^*$ equipped with the compact-open topology.\n  Van Douwen proved it is consistent for $\\sigma$ and $\\sigma^{-1}$ not to be isomorphic. Whether it is also consistent for them to be isomorphic is an open problem. The theorem stated above can be thought of as a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09907","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"}