User blog:Ubersketch/n-dinals

Not even sure why I did this but here we go.

First, we will define the concept of a "collection."

0-sets can contain 0-sets but not 0-classes. 0-classes can contain 0-sets but not 0-classes.

1-sets can contain 0-sets, 0-classes, and 1-sets but not 1-classes. 1-classes can contain 0-sets, 0-classes, and 1-sets, but not 1-classes.

2-sets can contain 0-sets, 0-classes, 1-sets, 1-classes, and 2-sets but not 2-classes. 2-classes can contain 0-sets, 0-classes, 1-sets, 1-classes, and 2-sets, but not 2-classes.

In general.

0-sets are sets.

n-sets cannot contain n-classes but can contain m-sets and l-classes where m>=n and l>n, and are well-founded.

n-classes cannot contain n-classes but can contain m-sets and m-classes where m>n, and are well-founded.

We can define n-dinals similarly to von Neumann universes as transitive collections.

0-dinals are transitive 0-sets.

n-dinals cannot biject to any m-set or m-class, are greater than any m-dinal, where m>n, and are transitive.

Can't wait for someone to somehow make an "OCF" out of this.