User blog:Nayuta Ito/What We've Agreed on Stage Cardinal

Here, I'm going to write only what we've agreed on.

κ is any ordinal, including stage one.


 * 1) S(1)=Ω
 * 2) S(κ+1) is the next cardinal after S(κ)
 * 3) S(κ+T) does NOT the first fixed point of α→S(κ+α).
 * 4) The n-th fixed point of α→S(κ+α) is denoted by ψ_(S(κ+T))(n),
 * 5) S(κ+T) is the first fixed point of α→ψ_(S(κ+T))(α).

Have we already agreed on larger cardinals (Specifically, S(T^2) and larger)?