[sz]

I was wondering what subfield coined the label $\Pi_2$, specifically. I haven't looked much into the structure of propositions and proofs per se, and I'm curious about what can be said about it.

[pohl]

That is an excellent question. I've only seen capital pi used for repeated multiplication. I, too, would like to know what it means in this context.

I don't know if you missed it, but the author links to a PDF that mentions this notation in the abstract. I haven't had a chance to digest it, though:

http://www.cs.cmu.edu/~crary/819-f09/Murthy91.pdf

Edit: Behold...

http://en.wikipedia.org/wiki/Descriptive_set_theory

http://en.wikipedia.org/wiki/Arithmetical_hierarchy

http://en.wikipedia.org/wiki/Analytical_hierarchy