User blog comment:Kyodaisuu/English description of Fish numbers/@comment-25418284-20131102173245/@comment-24061664-20131103170055

How many characters are required to express a number larger than Rayo(Rayo(10^100)) in FOST and OFOST (oracle-implemeted FOST with Rayo oracle) ?

(1) FOST

In FOST, it requires more than Rayo(10^100) numbers, becaues Rayo(Rayo(10^100)) is larger than any number expressed by FOST expression in less than Rayo(10^100) numbers.

(2) OFOST

Let FOST(3,10^100) be a FOST expression which forces 3rd object to be a specified number larger than 10^100. Then, Rayo(Rayo(10^100)) can be expressed as (f(3)=2)∧(f(2)=1)∧(FOST(3,10^100)). It is just 20 characters longer than FOST(3,10^100). As it would be easy to express a number larger than 10^100 in 9980 characters of FOST, OFOST with 10000 characters can express Rayo(Rayo(10^100)).

FOST requires more than Rayo(10^100) characters, while OFOST requires only 10000 characters. Therefore, OFOST is much stronger than FOST.