{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/grzegorczyk-sequence","title":"Grzegorczyk sequence","arxiv_id":"1811.09958","date":"2018-11-25","proceeding":null,"authors":["Toshiyasu Arai"],"abstract":"Natural numbers are represented by Grzegorczyk functions. The representation is implicit in the technique of H. Friedman. An iterated base-shift in the representation with subtracting 1 yields a sequence, Grzegorczyk sequence. It is shown that the termination of the sequence is independent from the first order arithmetic PA. We follow M. Rathjen in the proof of the independence.","url_abs":"https://arxiv.org/abs/1811.09958v1","url_pdf":"https://arxiv.org/pdf/1811.09958v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"grzegorczyk-sequence","repo_url":"https://github.com/koteitan/grzeseq","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}