{"paper":{"title":"The Axiom of Double Complement and its opposites","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Hanul Jeon, James E. Hanson","submitted_at":"2026-05-30T19:26:04Z","abstract_excerpt":"Powell introduced the Axiom of Double Complement ($\\mathsf{DCom}$) to give his double-negation interpretation of $\\mathsf{ZF}$ into $\\mathsf{IZF_{Rep}}$. However, the consistency, strength, and compatibility of $\\mathsf{DCom}$ remain open problems. This article aims to survey the compatibility and consistency strength of $\\mathsf{DCom}$, its consequence and opposites, which will be named $\\mathsf{NDCom}$ and $\\mathsf{ADCom}$. We will also develop Lubarsky's Kripke models over $\\mathsf{CZF}$ to derive these results.\n  We will show that $\\mathsf{DCom}$ proves the Powerset axiom over $\\mathsf{CZF"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00861","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00861/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}