{"paper":{"title":"Reversible Disjoint Unions of Well Orders and Their Inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. Kurili\\'c, Nenad Mora\\v{c}a","submitted_at":"2017-11-19T17:11:42Z","abstract_excerpt":"A poset ${\\mathbb{P}}$ is called reversible iff every bijective homomorphism $f:{\\mathbb{P}} \\rightarrow {\\mathbb{P}}$ is an automorphism. Let ${\\mathcal{W}}$ and ${\\mathcal{W}} ^*$ denote the classes of well orders and their inverses respectively. We characterize reversibility in the class of posets of the form ${\\mathbb{P}} =\\bigcup _{i\\in I}{\\mathbb{L}} _i$, where ${\\mathbb{L}} _i, i\\in I$, are pairwise disjoint linear orders from ${\\mathcal{W}} \\cup {\\mathcal{W}} ^*$. First, if ${\\mathbb{L}} _i \\in {\\mathcal{W}}$, for all $i\\in I$, and ${\\mathbb{L}} _i \\cong \\alpha _i =\\gamma_i+n_i\\in Ord$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07053","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"}