{"paper":{"title":"Maximally Embeddable Components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milos S. Kurilic","submitted_at":"2013-03-11T17:26:29Z","abstract_excerpt":"We investigate the partial orderings of the form (P(X),\\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally embeddable and satisfy an additional condition related to connectivity, then the poset (P(X),\\subset) is forcing equivalent to a finite power of (P(\\omega)/Fin)^+, or to (P(\\omega \\times \\omega)/(Fin \\times Fin))^+, or to the direct product (P(\\Delta)/ED_fin)^+ \\times ((P(\\omega)/Fin)^+)^n, for some n \\in \\omega. In particular we obtain forcing equivalents of the pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2591","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"}