I like geometry. Let's start with Hilbert's axioms for Euclidean geometry and prove a couple theorems and a couple statements that look like they are theorems but are demonstrably false.
At 10:08 AM 12/23/2011, Joe Niederberger wrote: > >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).