  The concept of definability of physical fields within a set-theoretical
foundation is introduced. We propose an axiomatic set theory and show the
Schroedinger equation and, more generally, a nonlinear sigma model come
naturally out of the mathematics of this theory when a physical null postulate
is added. Space-time is relational in this theory and quantization of the field
proves to be equivalent to definability. Some additional examples of
applicability to physics are given.
