User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-24920136-20170404223258/@comment-28606698-20170405173417

Thanks, and I wish you the best. If you mean naming scheme for numbers, as you know last year I did naming scheme for numbers less than and greater than BHO, which are obtained via FGH, and I think this amount of names is enough. But since poor standatization in the set theory, those numbers were not well-defined till FS are described. For example, omega is defined as smallest number, which is greater than all natural numbers. O'k but we can define omega[n]=n, we also can write omega[n]=Rayo(n) in both cases the limit of those sequences will be omega according its definition, thus both FS are valid. As I understand definitions of OCF's not allow to get automatically system of rules for FS. Thus FGH without FS allows to show only scale of number, but if FS are known then we can generate with help of FGH a well-defined numbers and, using hypotetical infinite computer, we can calculate full decimal expansion of such numbers. So, it is actual. Several days ago, after this post was publishing, I found that Deedlit already has done titanical work and defined FS up to BHO and even much further. Nevertheless in future I want to research FS for my psi'-function beyond BHO.