Recursive definitions on surreal numbers
逻辑
2007-05-23 v1 环与代数
摘要
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.
引用
@article{arxiv.math/0612234,
title = {Recursive definitions on surreal numbers},
author = {Antongiulio Fornasiero},
journal= {arXiv preprint arXiv:math/0612234},
year = {2007}
}