{"paper":{"title":"Vaught's Conjecture for Almost Chainable Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. Kurili\\'c","submitted_at":"2019-05-14T11:44:47Z","abstract_excerpt":"A structure ${\\mathbb Y}$ of a relational language $L$ is called almost chainable iff there are a finite set $F \\subset Y$ and a linear order $<$ on the set $Y\\setminus F$ such that for each partial automorphism $\\varphi$ (i.e., local automorphism, in Fra\\\"{\\i}ss\\'{e}'s terminology) of the linear order $\\langle Y\\setminus F, < \\rangle$ the mapping ${\\mathrm{id}} _F \\cup \\varphi$ is a partial automorphism of ${\\mathbb Y}$. By a theorem of Fra\\\"{\\i}ss\\'{e}, if $|L|<\\omega$, then ${\\mathbb Y}$ is almost chainable iff the profile of ${\\mathbb Y}$ is bounded; namely, iff there is a positive integer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05531","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"}