High Quality Content by WIKIPEDIA articles! In mathematics, the Veblen functions are a hierarchy of functions from ordinals to ordinals, introduced by Oswald Veblen in Veblen (1908). If ¿0 is any continuous strictly increasing function from ordinals to ordinals, then for any non-zero ordinal ¿, ¿¿ is the function enumerating the common fixed points of ¿¿ for ¿
High Quality Content by WIKIPEDIA articles! In mathematics, the Veblen functions are a hierarchy of functions from ordinals to ordinals, introduced by Oswald Veblen in Veblen (1908). If ¿0 is any continuous strictly increasing function from ordinals to ordinals, then for any non-zero ordinal ¿, ¿¿ is the function enumerating the common fixed points of ¿¿ for ¿<¿. These functions are all continuous strictly increasing functions (i.e. normal functions) from ordinals to ordinals. The fundamental sequence of an ordinal with cofinality ¿ is a distinguished strictly increasing ¿-sequence which has the ordinal as its limit. If one has fundamental sequences for ¿ and all smaller limit ordinals, then one can create an explicit constructive bijection between ¿ and ¿, (i.e. one not using the axiom of choice). Here we will describe fundamental sequences for the Veblen hierarchy of ordinals. The image of n under the fundamental sequence for ¿ will be indicated by ¿.