How to rebind "special meaning" of C-u to a different key?

Question

Excerpt from GNU Emacs manual:

C-u alone has the special meaning of “four times”: 
it multiplies the argument for the next command by four. 
C-u C-u multiplies it by sixteen.
Thus, C-u C-u C-f moves forward sixteen characters.

Is there a way to get this multiplication by sixteen when rebinding universal-argument to a different key? I did the following:

(global-set-key (kbd "C-i") 'universal-argument)

But when I press C-i C-i a only 4 copies of a are inserted, not 16 (if I rebind universal-argument back to C-u then I get 16 copies as advertised in the manual).

Answer 1

Add at least one additional definition:

(global-set-key (kbd "C-i") 'universal-argument)

(define-key universal-argument-map (kbd "C-i") 'universal-argument-more)

See additional universal-... definitions in both bindings.el and simple.el that may be rebound if so desired.