Models and Modeling in Science: the role of metamathematics

The use of models of scientific theories should not be done without qualifications about the mathematics being used to build the models. This looks obvious, at least for logicians, but generally, it is not to the philosopher of science. Thus, some details about this point seem useful for both. Since any quick revision in the literature shows that in most cases, mainly after the raising of the semantic approach (to scientific theories), the models are taken to be set-theoretical structures, in discussing the issue we shall be concerned more with set theories, the locus where the play is usually developed (yet sometimes unconsciously).