Veblen Function
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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 ...
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 .
