The model theory of modules over a ring depends essentially on the positive-primitive (pp) formulas. The sets defined by pp formulas are exactly those which are preserved by homomorphisms between modules and the pure-exact structure on a module category is determined by the pp formulas. Thus model theory and algebra fit together well in the additive context. I will discuss these basic ideas and then concentrate on pure-injective modules, these being the modules which realise all pp-types, and their various uses.
Please send an email to: r.zoghi@gmail.com to join this lecture.