  The concept of definability of quantum fields in a set-theoretical foundation
is introduced. We propose an axiomatic set theory and then derive a nonlinear
sigma model and the Schroedinger equation in a Lagrangian form; this follows
naturally from a null postulate which expresses symmetry of action.
Definability in this theory is necessary and sufficient for quantum mechanics.
Space-time proves to be relational and the fields are free of singularities
