{"paper":{"title":"Homomorphisms Between Rings with Infinitesimals and Infinitesimal Comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Emanuele Bottazzi","submitted_at":"2019-02-16T09:45:43Z","abstract_excerpt":"We examine an argument of Reeder suggesting that the nilpotent infinitesimals in Paolo Giordano's ring extension of the real numbers $^{\\bullet}\\mathbb{R}$ are smaller than any infinitesimal hyperreal number from Abraham Robinson's nonstandard analysis $^\\ast\\mathbb{R}$. Our approach consists in the study of two canonical order-preserving homomorphisms taking values in ${^{\\bullet}\\mathbb{R}}$ and in ${^\\ast\\mathbb{R}}$, respectively, and whose domain is Henle's extension of the real numbers in the framework of \"non-nonstandard\" analysis. In particular, we will show that there exists a nonzero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06076","kind":"arxiv","version":2},"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"}