User blog:Ubersketch/Lexicographic ordinal notation up to the Bachmann-Howard ordinal

The notation is based on the following OCF: To convert expressions to lexicographical strings, you do the following: A standard expression looks like:
 * \(C_0(\alpha,\beta) = \beta\cup\{0\}\)
 * \(C_{n+1}(\alpha,\beta) = \{\gamma+\delta|\gamma,\delta\in C_n(\alpha,\beta)\}\)
 * \(C(\alpha,\beta) = \bigcup_{n<\omega} C_n(\alpha,\beta)\)
 * \(\psi_\pi(\alpha) = \min\{\beta<\pi|C(\alpha,\beta)\cap\pi\subseteq\beta\}\)
 * \(0\rightarrow A\)
 * \(\alpha+\beta\rightarrow\alpha\beta B\)
 * \(\psi(\alpha)\rightarrow C\alpha\)
 * \(\Omega^\alpha\beta\rightarrow D\alpha\beta\)

W.I.P.