This seems to be a common exercise among many books (cf. Enderton, p. 28, van Dalen, p. 45, Hinman, p. 51, Chang and Keisler, p. 18), with some minor variations among them. The idea is simple. Say ...
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 ...