{"paper":{"title":"Encoding Sets as Real Numbers (Extended version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alberto Policriti, Domenico Cantone","submitted_at":"2018-06-25T08:53:33Z","abstract_excerpt":"We study a variant of the Ackermann encoding $\\mathbb{N}(x) := \\sum_{y\\in x}2^{\\mathbb{N}(y)}$ of the hereditarily finite sets by the natural numbers, applicable to the larger collection $\\mathsf{HF}^{1/2}$ of the hereditarily finite hypersets. The proposed variation is obtained by simply placing a `minus' sign before each exponent in the definition of $\\mathbb{N}$, resulting in the expression $\\mathbb{R}(x) := \\sum_{y\\in x}2^{-\\mathbb{R}(y)}$. By a careful analysis, we prove that the encoding $\\mathbb{R}_{A}$ is well-defined over the whole collection $\\mathsf{HF}^{1/2}$, as it allows one to u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09329","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"}