{"paper":{"title":"Reversible Sequences of Cardinals, Reversible Equivalence Relations, and Similar Structures","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":"2017-09-27T13:22:01Z","abstract_excerpt":"A relational structure ${\\mathbb X}$ is said to be reversible iff every bijective endomorphism $f:X\\rightarrow X$ is an automorphism. We define a sequence of non-zero cardinals $\\langle \\kappa_i :i\\in I\\rangle$ to be reversible iff each surjection $f :I\\rightarrow I$ such that $\\kappa_j =\\sum_{i\\in f^{-1}[\\{ j \\}]}\\kappa_i$, for all $j\\in I $, is a bijection, and characterize such sequences: either $\\langle \\kappa_i :i\\in I\\rangle$ is a finite-to-one sequence, or $\\kappa_i\\in {\\mathbb N}$, for all $i\\in I$, $K:=\\{ m\\in {\\mathbb N} : \\kappa_i =m $, for infinitely many $i\\in I \\}$ is a non-empty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09492","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"}