The formula for is actually a special case of the formula for a limit ordinal. Alternatively, you can do them all at once:
The axiom of foundation in ZFC is equivalent to the statement that every set is an element of for some ordinal . The rank of a set is defined to be the least for which (this is well-defined since the ordinals are well-ordered).
Revised on April 11, 2009 05:34:03
by Toby Bartels