User:Rpakr/Ordinal Address Notation Analysis

Ordinal Address Notation

Definition
Rule 1. \(\lbrace\rbrace=0\) Rule 2. \(\lbrace\#,0\rbrace=\lbrace\#\rbrace+1\) Rule 3. If \(cof(\alpha)=\omega\), \(\lbrace\#,\alpha\rbrace[n]=\lbrace\#,\alpha[n]\rbrace\) Rule 4. If \(cof(\alpha)=1\), \(\lbrace\#,\beta,@,\alpha\rbrace[n]=\lbrace\#,\beta,@,\beta,@,\cdots,\beta,@,\rbrace\) with n \(\beta,@,\)s \(\beta<\alpha\) and every entry in \(@\) is bigger than or equal to \(\alpha\)