2006/12/09 by Antongiulio Fornasiero, Fornasiero, Antongiulio
Computer Science · Mathematics · #03C64 #03C65 #03H05 #12J15 #20F60 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Rings and Algebras (math.RA) #math.LO #math.RA #msc:03C64 #msc:03C65 #msc:03H05 #msc:12J15 #msc:20F60
paper · pdf · doi:10.48550/arxiv.math/0612234
arxiv created 2006/12/09 · openalex publication_date 2006/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let No be Conway's class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some "tameness" and uniformity condition, f must satisfy some interesting properties; in particular, the supremum of the class of element greater or equal to a fixed d in No is actually an element of No. For similar reasons, the concatenation function x:y cannot be defined recursively in a uniform way over polynomial functions.