User:Rpakr/Cardinal Space

Cardinal Space

ecl1, April 23rd 2018, discord:

"Think an infinite-dimensional space so that every spot in it is filled with an uncountable ordinal.

First row contains W, W_2, W_3, W_4, etc.

Second row contains I, I_2, I_3, etc.

Third row contains I(1,0), I(1,1), I(1,2), etc.

Fourth row contains I(2,0), I(2,1), I(2,2), etc.

... First row of second plane has M, M_2, M_3, etc.

Next row has M(1,n)

Next row has M(2,n)

...

Third plane contains N, N_2, N(1,0), ...

Fourth plane contains Xi[3], Xi[3]_2, Xi[3](1,0)...

Fifth plane contains Xi[4], Xi[4]_2, Xi[4](1,0)...

...

First row of second realm (3D space) contains K, K_2, ...

Next row has K(1,n)

Next row has K(2,n)

Next plane starts with the next level of mahloness after K

...

Next realm has the first 1-weakly compact

Next realm has the first 2-weakly compact

...

Next 4D space has the ultimate cardinal (stage-4), diagonalizer for n-weakly compacts

Next 5D space has the stage-5 cardinal

..."

T is stage cardinal.