{"paper":{"title":"Taming Koepke's Zoo II: Register Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl","submitted_at":"2019-07-22T18:26:34Z","abstract_excerpt":"We study the computational strength of resetting $\\alpha$-register machines, a model of transfinite computability introduced by P. Koepke in \\cite{K1}. Specifically, we prove the following strengthening of a result from \\cite{C}: For an exponentially closed ordinal $\\alpha$, we have $L_{\\alpha}\\models$ZF$^{-}$ if and only if COMP$^{\\text{ITRM}}_{\\alpha}=L_{\\alpha+1}\\cap\\mathfrak{P}(\\alpha)$, i.e. if and only if the set of $\\alpha$-ITRM-computable subsets of $\\alpha$ coincides with the set of subsets of $\\alpha$ in $L_{\\alpha+1}$. Moreover, we show that, if $\\alpha$ is exponentially closed and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09513","kind":"arxiv","version":8},"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/1907.09513/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"}