2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119889Let 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.LogicRings and Algebras03C64, 03C65, 03H05, 12J15, 20F60text