{"paper":{"title":"Random graphs and Lindstrom quantifiers for natural graph properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saharon Shelah, Simi Haber","submitted_at":"2015-10-22T10:56:18Z","abstract_excerpt":"We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P, is there a language of graphs able to express P while obeying the zero-one law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey the zero-one law. On the other hand we show that in any (semiregular) language strong enough to express Hamiltonicity one can interpret arithmetic and thus the zero-one law fails miserably. This answers a question of Blass and Harary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06574","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"}