User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20131114015734/@comment-5529393-20131116085248

Actually, the θ function can have uncountable ordinals in the second argument, and in fact this is essential for the power of the notation. θ(Ω,Ω) is perfectly legal. However Wythagoras was using $$\vartheta$$, which is a one-variable function.