Recursive definitions on surreal numbers

Details Recursive definitions on surreal numbers Recursive definitions on surreal numbers

2006-12-09

arxiv.org/abs/math/0612234v1

Mathematics

Logic

Scientific paper

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.

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