>Do your "garden variety mathematical theories" include >things like number theory, abstract algebra and geometry?
I was being a bit tongue in cheek. To NOT be in the class of "effectively generated theory" the formal theory in question must have axioms that comprise a non-recursively enumerable set. Truly exotic, as I said. Actually, I'm not really aware of any theories of algebra or geometry that are not "effectively generated" (i.e., garden variety).