seeing I now have stuff on the wiki, my real name is Lawrence Hollom. I have also slightly changed my notation quite a lot. This is due to a pretty large misinformation from a website that now refuses to turn up on searches so that I can mention this to the person who owns it. This lead me to believe a completely incorrect definition on how ordinals above zeta 0 worked. The changes I have made to my notation now bring it up to the power I thought it was at before. The changes are (briefly) summed up below (if you want more detail, look at my website):
- The first row remains unchanged.
- The second row works like the veblen hierarchy with the entries in the opposite order and a default of 1.
- The third row and higher work in a similar way to the second row, but using an ordinally nesting hierarchy.
- If the active entry's row has only one entry, it decreases by one and changes the previous block (block before the largest block that the active entry is the first entry in) to have dimensions and superdimensions etc. of an ordinally S(position with all coordinates - 1)NH (will be array in there, so needs larger parts of the nesting hierarchy), and set all of the entries in these to be n.
- An ordinally NH means that there remains only 1 "n!", even if the entire thing was to be written out in full.
Sorry if I have made anyone's work on the higher rows completely useless, it made mine useless too. I believe that the second row will work just like the extended veblen function, and so takes the 2nd row up to a limit of f_SVO(n). Because a 3rd row with only 1 entry will set the number of inputs on the previous row to a S2NH of themselves with all inputs in the 2nd row set to n, I believe that this is equivalent to or greater than f_LVO(n). All comments are appreciated, thanks for all the feedback on the previous post.
Btw, what are the large and small veblen ordinals in different ordinal notations? I have found contradicting wikipedia pages, one here, about 1/3 of the way down, under the heading "beyond the Feferman-Schütte ordinal", and the other here, on the LVO, and another on the SVO here. The pages on the LVO and SVO say one thing, and the one on ordinal collapsing functions another. Thanks in advance.