{"paper":{"title":"On $\\alpha$-largeness and the Paris-Harrington principle in $\\mathrm{RCA}_0$ and $\\mathrm{RCA}_0^{\\displaystyle{*}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy","submitted_at":"2016-11-28T05:37:12Z","abstract_excerpt":"We examine, within $\\mathrm{RCA}_0$, the treatment by Ketonen and Solovay on the use of $\\alpha$-largeness for giving an upper bound for the Paris--Harrington principle. This proof works fine in $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for every fixed standard dimension. We also show how to modify the arguments to work within $\\mathrm{RCA}_0^{\\displaystyle{*}}$ for unrestricted dimensions. To the author's knowledge, this is the first time that it is confirmed that the treatment can be done within $\\mathrm{EFA}$ without some transfinite induction added."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08988","kind":"arxiv","version":4},"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"}