User:Rpakr/Ordinal Address Notation Analysis

Definition
Rule 1. \(\{\}=0\)

Rule 2. \(\{\#,0\}=\{\#\}+1\)

Rule 3. If \(cof(\alpha)=\omega\), \(\{\#,\alpha\}[n]=\{\#,\alpha[n]\}\)

Rule 4. If \(cof(\alpha)=1\), \(\{\#,\beta,@,\alpha\}[n]=\{\#,\beta,@,\alpha-1,@,\alpha-1,\cdots,@,\alpha-1\}\) with n \(@,\alpha-1\)s

\(\beta<\alpha\) and every entry in \(@\) is bigger than or equal to \(\alpha\)

Up to \(\varepsilon_1\)
We start using rule 3 here.