U function

U(n) is an extremely fast-growing function devised by Chris Bird. It is the fastest function he defined as of June 2013.
Bird was analyzing isomorphism between his separators and ordinals using some unspecified variant of \(\theta\) ordinal collapsing function, and roughly it can be said that the limit ordinal measuring strength of this function is \(\theta(\Omega_\omega)\). It is not known how does it compare with fast-growing hierarchy and its cousins because the system of fundamental sequences should be fixed and rigorous analysis should be done. However, it is believed that the growth rate should be around \(f_{\theta(\Omega_\omega)}(n)\) in the fast-growing hierarchy whatever fundamental sequences are.
Using Bird's Hierarchical Hyper-Nested Array Notation, \(U(n) = \{3,n [1 [1 [1 [ \cdots [1 [1 /_n 1 /_n 2] 2] \cdots ] 2] 2] 2] 2\}\) (with n sets of square brackets).
== See also ==
*H function
*S function
== Sources ==
ja:U関数
Category:Functions
Category:Higher computable level