I'm studying Model Theory: an introduction by David Marker and more specifically doing the exercises of chapter 2 ("Basic techniques"). In several of these exercises, one is asked to build new models ...
Take first-order Peano Arithmetic PA. We know that Gentzen proved PA consistent. Now, if one sets for example $\varphi$ to represent Fermat's theorem in FO, would proving PA+$\varphi$ consistent be ...
Various mathematical areas of research evolved from a wide and diverse range of questions. Many are physical in nature or come from informatics/computer science, some are procedural or optimization ...