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On the other hand, we prove that if lambda = mu^+, mu = mu^{< mu}, and a forcing axiom holds (and aleph_1^L= aleph_1 if mu = aleph_0), then there is a sentence of L_{lambda lambda} which separates K^0_lambda and K^1_lambda ."},"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":"math/9706225","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1997-06-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"0beb055cad072304375beeb4ab677d91ee5293b45311bf16acf488bbdcf92fbf","abstract_canon_sha256":"df45578559fd2badd6f0965c0b695bc8b3ba3f4064712e940888e502b34d6301"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:35.128979Z","signature_b64":"Ymm3ABS0nOf246uX6kYlYqdrpJwhXjmOgkdn5VS9NLp8MozbHhVOnJ4/GyqBvzJDd8jv/KukVM0nFsMX7ILIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b21bec878164bf897648bca294629cb9d0ff355bf167e5c75077db40ffda6360","last_reissued_at":"2026-05-18T01:05:35.128292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:35.128292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary sets and infinitary logic","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jouko V\\\"a\\\"an\\\"anen, Saharon Shelah","submitted_at":"1997-06-15T00:00:00Z","abstract_excerpt":"Let K^0_lambda be the class of structures < lambda,<,A>, where A subseteq lambda is disjoint from a club, and let K^1_lambda be the class of structures < lambda,<,A>, where A subseteq lambda contains a club. 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