In this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime ...

OF all the branches of philosophy, logic alone has had the distinction of being claimed by the exact sciences as one of them. The event is of recent occurrence; in fact, it has happened only since ...

We show that every nonzero $\Delta _{2}^{0}$ e-degree bounds a minimal pair. On the other hand, there exist $\Sigma _{2}^{0}$ e-degrees which bound no minimal pair. Journal Information The Journal of ...