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We show that a complete theory ${\\mathcal T}$ having infinite models is monomorphic iff it has a countable monomorphic model and confirm the Vaught conjecture for monomorphic theories. More precisely, we prove that if ${\\mathcal T}$ is a complete monomorphic theory having infinite models, then the number of its non-isomorphic countable models, $I({\\mathcal T},\\omega )$, is either equal to $1$ or"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.07210","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-17T19:22:47Z","cross_cats_sorted":[],"title_canon_sha256":"521ce55828e4bd810c96ddde27fe9b478926d4c103391935b605ff5f57709cf9","abstract_canon_sha256":"5241e9f4ba5cf49dcff5d192fce3e7f08728abfd8e5c6b77a99a2d90fcbd65de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.847386Z","signature_b64":"sEDin+BCVVlGv3mOwb/lJQNVOBgkv/Ed59oDtSO61mNEfSzLrtsEa15xCIs0USUAzAaZCHnU6mpCm8xmq9nqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5622822a0f5b35c6f43cc513bcc6b945bcdb737aedb35f4933e45f8f9f00112","last_reissued_at":"2026-05-17T23:58:55.846850Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.846850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vaught's Conjecture for Monomorphic Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milo\\v{s} S. 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