User blog comment:LittlePeng9/Higher order set theory/@comment-10429372-20140926180316/@comment-10429372-20140926181739

I think w1DEF can be defined as following:


 * The smallest ordinal that cannot be defined using any formal language.

There must be systems stronger than OOST, I believe, so, the growth rate can't be w1DEF.

Also, how about (O*2)OST, (e(O+1))OST, and then the limit of ordinals based on O?

O is some sort of absolute infinity. But actually it is the following ordinal:


 * Τhe first ordinal such that for all ordinals β>α βOST has β as largest definable ordinal.