{"paper":{"title":"Automorphisms of models of set theory and extensions of NFU","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zachiri McKenzie","submitted_at":"2013-09-18T12:56:21Z","abstract_excerpt":"In this paper we exploit the structural properties of standard and non-standard models of set theory to produce models of set theory admitting automorphisms that are well-behaved along an initial segment of their ordinals. $\\mathrm{NFU}$ is Ronald Jensen's modifcation of Quine's `New Foundations' set theory that allows non-sets into the domain of discourse. The axioms $\\mathrm{AxCount}$, $\\mathrm{AxCount}_\\leq$ and $\\mathrm{AxCount}_\\geq$ each extend $\\mathrm{NFU}$ by placing restrictions on the cardinality of a finite set of singletons relative to the cardinality of its union. Using the resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4631","kind":"arxiv","version":2},"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"}