User blog comment:Deedlit11/Ordinal Notations III: Collapsing Higher Cardinalities/@comment-11227630-20160501075609/@comment-5529393-20160504095823

You're right, it should be $$C_0(\alpha, \beta) = \beta \cup \lbrace 0 \rbrace$$ to be consistent with earlier versions;  I'm not sure why I left it out. $$\Omega_0$$ usually means 0.