User:Augigogigi/SbOCF

sbocf is bla bla bla limit is bla bla bla

Definition

• \( T_{a}(b) = \)
• \( \tau(a) = \)
• \( \kappa(0) = \)

Fundamental Sequences

bla bla bla function:

\begin{align} [] : \text{S} \times \mathbb{N} \rightarrow& \text{S} \\ (\text{S},n) \mapsto& \text{S}[n] \end{align}

bla bla bla bla bla

Analysis

Expression	Shorthand
\( \tau(a) \)	\( \Omega_{a} \)
\( \tau(B+a) \)	\( M_{a} \)
\( \tau(B\cdot2+a) \)	\( N_{a} \)
\( \tau(B^{2}+a) \)	\( G_{a} \)

SbOCF	Ordinal	Xi	BMS
\( T_{\tau(0)}(0) \)	\( 1 \)	-	\( (0) \)
\( T_{\tau(0)}(1) \)	\( \omega \)	-	\( (0)(1) \)
\( T_{\tau(0)}(2) \)	\( \omega^{2} \)	-	\( (0)(1)(1) \)
\( T_{\tau(0)}(T_{\tau(0)}(0)) \)	\( \omega^{\omega} \)	-	\( (0)(1)(2) \)
\( T_{\tau(0)}(T_{\tau(0)}(T_{\tau(0)}(0))) \)	\( \omega^{\omega^{\omega}} \)	-	\( (0)(1)(2)(3) \)
\( T_{\tau(0)}(\tau(0)) \)	\( \varepsilon_{0} \)	-	\( (0,0)(1,1) \)
\( T_{\tau(0)}(\tau(0)+1) \)	\( \varepsilon_{0}\cdot\omega \)	-	\( (0,0)(1,1)(1,0) \)
\( T_{\tau(0)}(\tau(0)+T_{\tau(0)}(0)) \)	\( \varepsilon_{0}\cdot\omega^{\omega} \)	-	\( (0,0)(1,1)(1,0)(2,0) \)
\( T_{\tau(0)}(\tau(0)+\tau(0)) \)	\( \varepsilon_{0}^{2} \)	-	\( (0,0)(1,1)(1,0)(2,1) \)
\( T_{\tau(0)}(\tau(0)\cdot\omega) \)	\( \varepsilon_{0}^{\omega} \)	-	\( (0,0)(1,1)(1,1) \)