User blog:Bubby3/nth order cardinals and n-seperators.

In Strong Array Notation DAN, it has the idea of n-seperators. Tehy represent the 'level' of a seperator. For example, the grave accent and every seperator containing a double comma is a 1-seperator. 2-seperators are either double commas or seperators directly containing triple-commas. The level of a seperator is defined as follows. Clvl stands for comma level

Clvl of a comma is 0 and the Clvl of a grave accent is 1 Clvl(,...,) with n commas is n for n > 1

Clvl({a1A1a2...an-1An-1an}}, where a's are numbers and A's are separators = Max(Max(Clvl(A1),Clvl(A2)...Clvl(An-1),Clvl(An))-1,0). So the comma level of a separator is one less than the comma level of the separator with the highest comma level within that separator, and 0 if the the highest comma level inside that separator is 0.

A separator like {2,,2} is not a 1-seperator despite having a comma level of 1. A separator is only an n-seperator if there are only 1's before the first instance of the n-1-seperator.

Inthis blog post, I talk about the B cardinal, and higher order B cardinals. Any regular cardinal is a first-order cardinal, B and A_2(0,a) are 2nd order cardinals, and B{n} is a 1+nth order cardinal.

My idea of 2nd order cardinal might correspond with an X cardinal, where X is a large cardinal property, and 2+nth order cardinals are 0-X cardinals.