Abstract

We present familiar principles involving objects and classes (of objects), pairing (on objects), choice (selecting elements from classes), positive classes (elements of an ultrafilter), and definable classes (definable using the preceding notions). We also postulate the existence of a divine object in the formalized sense of lying in every definable positive class. ZFC (even extended with certain hypotheses just shy of the existence of a measurable cardinal) is interpretable in the resulting system. This establishes the consistency of mathematics relative to the consistency of these systems. Measurable cardinals are used to interpret and prove the consistency of the system. Positive classes and various kinds of divine objects have played significant roles in theology.