{"paper":{"title":"Asymptotic probabilities of extension properties and random $l$-colourable structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vera Koponen","submitted_at":"2012-04-11T14:25:29Z","abstract_excerpt":"We consider a set $\\mbK = \\bigcup_{n \\in \\mbbN}\\mbK_n$ of {\\em finite} structures such that all members of $\\mbK_n$ have the same universe, the cardinality of which approaches $\\infty$ as $n\\to\\infty$. Each structure in $\\mbK$ may have a nontrivial underlying pregeometry and on each $\\mbK_n$ we consider a probability measure, either the uniform measure, or what we call the {\\em dimension conditional measure}. The main questions are: What conditions imply that for every extension axiom $\\varphi$, compatible with the defining properties of $\\mbK$, the probability that $\\varphi$ is true in a memb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2460","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"}