{"paper":{"title":"An Easton-like Theorem for Zermelo-Fraenkel Set Theory with the Axiom of Dependent Choice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Anne Fernengel, Peter Koepke","submitted_at":"2018-12-03T18:33:15Z","abstract_excerpt":"We show that in the theory ZF + DC + for every cardinal {\\lambda}, the set of infinite subsets of {\\lambda} is well-ordered (i.e., Shelah's AX4), the {\\theta}-function measuring the surjective size of the powersets P({\\kappa}) can take almost arbitrary values on any set of uncountable cardinals. This complements our results from [FK16], where we prove that in ZF (without DC), any possible behavior of the {\\theta}-function can be realized; and answers a question of Shelah in [She16], where he emphasizes that ZF + DC + AX4 is a reasonable theory, where much of set theory and combinatorics is pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00960","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"}