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It is well-known that $\\mathsf{DC} \\Rightarrow \\mathsf{AC}_\\omega$. We study for which sets and under which hypotheses $\\mathsf{DC}(X) \\Rightarrow \\mathsf{AC}_\\omega (X)$, and then we show it is consistent with $\\ma"},"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":"2305.06676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2023-05-11T09:23:47Z","cross_cats_sorted":[],"title_canon_sha256":"d149820d896ebd6de5169fb8d7ca44b77951e2fe011b6448912cb347b45e4f0c","abstract_canon_sha256":"9a6a0e853c46bb9613f35001a81044323a343220fc10b23f3e3c6ae75372a33b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:46.940464Z","signature_b64":"WNos1Y+EITygj6XJ68NNOXYzf15QdsC5Ar6BseGCiQJfDORjFVREaynWoEyZ5aORauF27g2dJiIiOBBmjwDEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84ae42e961f7bf23161c2a2e5dbdb50f26272af02a8ade5ac9057c3ed8439336","last_reissued_at":"2026-07-05T09:56:46.939996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:46.939996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Does $\\mathsf{DC}$ imply $\\mathsf{AC}_\\omega$, uniformly?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alessandro Andretta, Lorenzo Notaro","submitted_at":"2023-05-11T09:23:47Z","abstract_excerpt":"The Axiom of Dependent Choice $\\mathsf{DC}$ and the Axiom of Countable Choice $\\mathsf{AC}_\\omega$ are two weak forms of the Axiom of Choice that can be stated for a specific set: $\\mathsf{DC}(X)$ asserts that any total binary relation on $X$ has an infinite chain, while $\\mathsf{AC}_\\omega (X)$ asserts that any countable collection of nonempty subsets of $X$ has a choice function. It is well-known that $\\mathsf{DC} \\Rightarrow \\mathsf{AC}_\\omega$. 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