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We compare |Seq(A)|, the cardinality of this set, to |P(A)|, the cardinality of the power set of A.\n  What is provable about these two cardinals in ZF? The main result of this paper is that\n  ZF |- for all A: |Seq(A)| not= |P(A)|\n and we show that this is the best possible result.\n  Furth"},"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/9308220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1993-08-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"0d5234fc0becc4a2a6a27798f6e4399d602cab491007c1d3c29922dc03fbab8b","abstract_canon_sha256":"492c96cc429369e1c7fc40ce1f5628b3cde1ca84fde351ab652f5780fc7e2eb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.949618Z","signature_b64":"u2f0573qG0MKMP0xK0QFUiwYcySYVp2FX3TinPqLIaGMzkL8+eDi35ME2sN7/zaxynmG/14mnziz3dTqXhY1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c7f138a2d5789e56acbc226b5d89a1983e5beffc808db287afd90031c5de4a5","last_reissued_at":"2026-05-18T01:05:51.949009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.949009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consequences of arithmetic for set theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Lorenz Halbeisen, Saharon Shelah","submitted_at":"1993-08-15T00:00:00Z","abstract_excerpt":"In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). 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