2006/11/21 by Mirco A. Mannucci, Mannucci, Mirco A., Rose M. Cherubin +2
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Geometric and Algebraic Topology #Logic in Computer Science (cs.LO) #Mathematical Dynamics and Fractals #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0611100
31 pages, Tennenbaum Memorial invited talk
arxiv created 2006/11/21 · openalex publication_date 2006/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core ideas proposed thus far. The second part of the paper presents a model of ultrafinitistic arithmetics based on the notion of fuzzy initial segments of the standard natural numbers series. We also introduce a proof theory and a semantics for ultrafinitism through which feasibly consistent theories can be treated on the same footing as their classically consistent counterparts. We conclude with a brief sketch of a foundational program, that aims at reproducing the transfinite within the finite realm.