User blog comment:Deedlit11/My humble extension of FOOT/@comment-5529393-20170117081155

Can we get some confirmation as to how Little Biggedon compares to BIG FOFT?

It looks to me like BIG FOFT is much bigger. Func0a is defined to be the same as Orda in FOOT; in particular, FOOT can define the truth predicate (with parameters) for FOST, hence so can FOFT10. Func10 is a function defined inductively, so that Func10(0) is the smallest ordinal b such that V and V_b satisfy the same sentences in the language of FOST augmented by a -> Func0a = Orda, i.e. the smallest ordinal b such that V and V_b satisfy the same ordinals of FOOT. So with this b we should be able to define a truth predicate for FOST. Next, Func1 0(1) is the second smallest b such that V and V_b satisfy the same sentences of FOOT, so we with this we can define a secondary truth predicate. Continuing in this fashion, Func10(a) should be the equivalent of 1+a truth predicates for FOST. Then, FOFT11 is a language where we can define the a'th truth predicate for any ordinal a that we can define, so it has the same power as Emlightened's language.

Little Biggedon is along the lines of "the largest number uniquely defined in FOFT11 using n symbols or less", except Emlightened uses quantifier rank rather than number of symbols. This uses this one 1-functional, and no functionals of order two or higher, so there is still a long way to go.