unique Definition and 2 Threads

I have 2 coupled PDEs: ##\nabla \cdot \vec J=0## and another one involving ##T## and partial derivatives of ##T## as well as ##\vec J##. Where the vector field ##\vec J=-\sigma \nabla V -\sigma S \nabla T##, ##\sigma## and ##S## are tensors (2x2 matrices). ##V## and ##T## are 2D scalar fields...

First-order logic is not categorical https://en.wikipedia.org/wiki/Categorical_theory meaning that infinite models cannot be defined uniquely just by axioms. Second-order logic is supposed to avoid this problem, which is one of the motivations for second-order arithmetic...