{"paper":{"title":"Constructing many atomic models in $\\aleph_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jerusalem), John T. Baldwin (U. Ill. Chicago), Michael C. Laskowski (U. of Maryland), Saharon Shelah (Hebrew University","submitted_at":"2015-03-01T17:37:20Z","abstract_excerpt":"We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\\omega_1,\\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are $2^{\\aleph_1}$ pairwise non-isomorphic atomic models of $T$, each of size $\\aleph_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00318","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"}