turkmath.org

As an illustration of some model-theoretic concepts, we consider a complete (logical) theory of mathematical actions. It is the so-called model-completion of the theory of actions, and the model-companion of the theory of group actions, while not itself being a theory of group actions. It shares certain properties with the theory of algebraically closed fields with distinguished generic multiplicative subgroup. Meanwhile, we do not forget mathematics itself as an (ethical) action.