Forum:Ultimate Ordinal Notation

Let start a basics.

The 1st set, contains a number of rules up to \(\epsilon_0\).

The 2nd set, contains a number of new rules up to \(\gamma_0\).

The 3rd set, contains a number of new rules up to SVO.

4th one, contains a number of new rules up to LVO.

And so on.

First I need a function: O

At 1st set:

1. O(A,0) = \(omega\)A

2. O(-1,A) = A

3. O(A,B) = \(omega\)A+B

And 2nd set:

Let @ has anything

4. O(@ \(\Omega\)A+1(B+1),C)[D+1] O(@ \(\Omega\)A+1B+OmegaA*O(@ \(\Omega\)A+1(B+1),C)[D],C)

5. O(@ \(\Omega\)A+1(B+1),C)[1] O(@ \(\Omega\)A+1B,C)

Anyone make a 3rd set of rules up to SVO? AarexTiao 18:14, September 8, 2013 (UTC)