  Hypercomputational formal theories will, clearly, be both structurally and
foundationally different from the formal theories underpinning computational
theories. However, many of the maps that might guide us into this strange realm
have been lost. So little work has been done recently in the area of
metamathematics, and so many of the previous results have been folded into
other theories, that we are in danger of loosing an appreciation of the broader
structure of formal theories. As an aid to those looking to develop
hypercomputational theories, we will briefly survey the known landmarks both
inside and outside the borders of computational theory. We will not focus in
this paper on why the structure of formal theory looks the way it does. Instead
we will focus on what this structure looks like, moving from hypocomputational,
through traditional computational theories, and then beyond to
hypercomputational theories.
